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Generalized Saphar decomposition of certain subclasses of generalized Drazin invertible linear relations 广义Drazin可逆线性关系某些子类的广义Saphar分解
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-11 DOI: 10.1007/s10476-025-00075-8
T. Álvarez, Y. Chamkha
{"title":"Generalized Saphar decomposition of certain subclasses of generalized Drazin invertible linear relations","authors":"T. Álvarez,&nbsp;Y. Chamkha","doi":"10.1007/s10476-025-00075-8","DOIUrl":"10.1007/s10476-025-00075-8","url":null,"abstract":"<div><p>For a Banach space, the notions of essentially left and right generalized Drazin invertible linear relations are introduced and studied. Then, characterizations of these classes by means of their generalized Saphar decompositions, accumulation and interior points of various spectra are given. Furthermore, sufficient conditions under which an essentially left (resp. right) generalized Drazin invertible linear relation be left (resp. right) Weyl generalized Drazin invertible are provided. In particular, we show that an everywhere defined closed linear relation with a nonempty resolvent set which has the SVEP at <span>(0)</span> (resp. its adjoint has the SVEP at <span>(0)</span>) is essentially left (resp. right) generalized Drazin invertible if and only if it is left (resp. right) Weyl generalized Drazin invertible. The corresponding spectra of such classes are also investigated and concrete examples are illustrated.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"363 - 388"},"PeriodicalIF":0.5,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weakly compact multipliers for some quantum group algebras 某些量子群代数的弱紧乘子
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-04 DOI: 10.1007/s10476-025-00076-7
M. Nemati, R. Esmailvandi, A. Ebrahimzadeh Esfahani
{"title":"Weakly compact multipliers for some quantum group algebras","authors":"M. Nemati,&nbsp;R. Esmailvandi,&nbsp;A. Ebrahimzadeh Esfahani","doi":"10.1007/s10476-025-00076-7","DOIUrl":"10.1007/s10476-025-00076-7","url":null,"abstract":"<div><p>Let <span>(mathbb{G})</span> be a locally compact quantum group. We study the\u0000existence of certain (weakly) compact right and left multipliers of the Banach al-\u0000gebra <span>(mathfrak{X} ^{*} )</span>, where <span>(mathfrak{X} )</span> is an introverted subspace of <span>(L^infty(mathbb{G}))</span> with some conditions, and\u0000relate them with some properties of <span>(mathbb{G})</span> such as compactness and amenability. For\u0000example, when <span>(mathbb{G})</span> is co-amenable and <span>(L^1(mathbb{G}))</span> is semisimple we give a characteri-\u0000zation for compactness of <span>(mathbb{G})</span> in terms of the existence of a nonzero compact right\u0000multiplier on <span>(mathfrak{X} ^{*} )</span>. Using this, for a locally compact group <span>({mathcal G})</span> we prove that <span>(mathbb{G}_a)</span> is\u0000compact if and only if there is a nonzero (weakly) compact right multiplier on <span>(mathfrak{X} ^{*} )</span>.\u0000Similar assertion holds for <span>(mathbb{G}_s)</span> when <span>({mathcal G})</span> is amenable.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"587 - 603"},"PeriodicalIF":0.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted anisotropic local Hardy spaces 加权各向异性局部Hardy空间
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-04 DOI: 10.1007/s10476-025-00077-6
Y. He
{"title":"Weighted anisotropic local Hardy spaces","authors":"Y. He","doi":"10.1007/s10476-025-00077-6","DOIUrl":"10.1007/s10476-025-00077-6","url":null,"abstract":"<div><p>In this paper, we introduce the weighted anisotropic local Hardy spaces <span>(h_{w, N}^p(mathbb{R}^n ; A))</span> with <span>(pin(0,1] )</span>, via the local non-tangential grand maximal function. We also\u0000establish the atomic decompositions for the weighted anisotropic local Hardy spaces <span>(h_{w, N}^p(mathbb{R}^n ; A))</span>. In addition, we obtain the duality between <span>(h_{w, N}^p(mathbb{R}^n ; A))</span> and the weighted anisotropic Campanato type spaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"525 - 545"},"PeriodicalIF":0.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Propagation of algebraic dependence and its applications 代数相关性的传播及其应用
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-04 DOI: 10.1007/s10476-025-00085-6
M. Liu, X. Dong
{"title":"Propagation of algebraic dependence and its applications","authors":"M. Liu,&nbsp;X. Dong","doi":"10.1007/s10476-025-00085-6","DOIUrl":"10.1007/s10476-025-00085-6","url":null,"abstract":"<div><p>We establish a criteria for the propagation of algebraic dependence of a set of differentiably non-degenerate meromorphic mappings from a complete and stochastically complete Kähler manifold <i>M</i> into a complex projective manifold, based on certain diffusion method. As its applications, we also consider the unicity problems for differentiably non-degenerate meromorphic mappings of <i>M</i> into a complex projective space in Nevanlinna theory. \u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"559 - 575"},"PeriodicalIF":0.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(L_prightarrow L_q) boundedness of Fourier multipliers (L_prightarrow L_q) 傅里叶乘数的有界性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-04 DOI: 10.1007/s10476-025-00078-5
M. Nursultanov
{"title":"(L_prightarrow L_q) boundedness of Fourier multipliers","authors":"M. Nursultanov","doi":"10.1007/s10476-025-00078-5","DOIUrl":"10.1007/s10476-025-00078-5","url":null,"abstract":"<div><p>This paper explores the boundedness of Fourier multipliers from \u0000<span>(L_p)</span> to <span>(L_q)</span>. We present new results that improve upon classical theorems due to Hörmander, Lizorkin, and Marcinkiewicz. In addition, we provide necessary conditions for the boundedness of Fourier multipliers. We introduce the concept of <span>(M)</span>-generalized monotone functions and sequences and derive criteria for the boundedness of Fourier multipliers corresponding to them.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"605 - 634"},"PeriodicalIF":0.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00078-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Monotonicity properties of classical functions and their q-analogues 经典函数及其q-类似函数的单调性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-06-04 DOI: 10.1007/s10476-025-00084-7
M. Bouali
{"title":"Monotonicity properties of classical functions and their q-analogues","authors":"M. Bouali","doi":"10.1007/s10476-025-00084-7","DOIUrl":"10.1007/s10476-025-00084-7","url":null,"abstract":"<div><p>We prove some new results and unify old ones on the complete monotonicity of functions including the gamma and digamma functions and their <i>q</i>-analogues. All of these results lead to new and interesting inequalities. Of particular interest, we obtain the following results:\u0000for all <span>(q&gt;0)</span>, <span>(qneq 1)</span>, <span>(x&gt;0)</span> and <span>(nin mathbb{N})</span>, we have\u0000</p><div><div><span>$$begin{aligned}logbig(frac{1-q^x}{1-q}big)- frac14frac{3q^x+1}{q^x-1}log qleqpsi_q(x)\u0000leqlogbig(frac{1-q^x}{1-q}big)-frac{1}2 frac{q^x}{q^x-1}log q, \u0000q^xbig(frac{log q}{q^x-1}big)^nP_{n-2}(q^x)+frac12q^xbig(frac{log q}{q^x-1}big)^{n+1}P_{n-1}(q^x)leq(-1)^{n+1}psi^{(n)}_q(x)\u0000 le q^xbig(frac{log q}{q^x-1}big)^nP_{n-2}(q^x)+q^xbig(frac{log q}{q^x-1}big)^{n+1}P_{n-1}(q^x).end{aligned}$$</span></div></div><p>\u0000where <span>(P_n(x))</span> is some polynomial of degree <i>n</i> to be defined later.</p><p>These inequalities are the <i>q</i>-analogues of the classical inequalities\u0000</p><div><div><span>$$frac1{2x}leqlog x-psi(x)leqfrac1{x},$$</span></div></div><p>\u0000and\u0000</p><div><div><span>$$frac{(n-1)!}{x^{n}}+frac{n!}{2x^{n+1}}leq (-1)^{n+1}psi^{(n)}(x)leqfrac{(n-1)!}{x^{n}}+frac{n!}{x^{n+1}},quad \u0000ngeq1, x&gt;0.$$</span></div></div></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"389 - 422"},"PeriodicalIF":0.5,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Riesz summation of rational Fourier-Chebyshev integral operators and approximations of functions with a power singularity 有理傅里叶-切比雪夫积分算子的Riesz和及幂奇点函数的逼近
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-04-22 DOI: 10.1007/s10476-025-00073-w
P. Patseika, Y. Rouba, K. Smatrytski
{"title":"On the Riesz summation of rational Fourier-Chebyshev integral operators and approximations of functions with a power singularity","authors":"P. Patseika,&nbsp;Y. Rouba,&nbsp;K. Smatrytski","doi":"10.1007/s10476-025-00073-w","DOIUrl":"10.1007/s10476-025-00073-w","url":null,"abstract":"<div><p>In the present paper Riesz sums of Fourier-Chebyshev rational integral operators with restrictions on the number of geometrically distinct poles are introduced. Approximation of the function <span>((1-x)^gamma)</span>, <span>(gamma in (0,1))</span>, by this method is considered. Estimates of pointwise and uniform approximation are established,\u0000as well as asymptotic expressions for the uniform approximation majorant. Additionally, the optimal values of the parameters of the approximating function, at which the rate of decrease of the majorant is the greatest are found. In the case of Riesz sums of a polynomial Fourier-Chebyshev series, approximation of functions satisfying the Lipschitz condition of order <span>(gamma)</span> on the segment <span>([-1,1])</span> is investigated.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"635 - 666"},"PeriodicalIF":0.5,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundedness of averaging operators in weighted variable exponent spaces of periodic functions 周期函数加权变指数空间中平均算子的有界性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-04-22 DOI: 10.1007/s10476-025-00074-9
O. L. Vinogradov
{"title":"Boundedness of averaging operators in weighted variable exponent spaces of periodic functions","authors":"O. L. Vinogradov","doi":"10.1007/s10476-025-00074-9","DOIUrl":"10.1007/s10476-025-00074-9","url":null,"abstract":"<div><p>Sufficient conditions for the uniform boundedness of the Steklov averaging operators in weighted variable exponent spaces of periodic functions are obtained.\u0000The boundedness of the Steklov averages was previously known if the exponent satisfies the Dini-Lipschitz condition and a local analogue of the Muckenhoupt condition holds. In this paper, the boundedness of the Steklov averages is established under certain Muckenhoupt type conditions solely, and the Dini-Lipschitz condition is not required. The norms of averaging operators are estimated explicitly.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 2","pages":"705 - 726"},"PeriodicalIF":0.5,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The generalized maximal operator on measures 测度上的广义极大算子
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2025-03-06 DOI: 10.1007/s10476-025-00066-9
J. Bonazza, M. Carena, M. Toschi
{"title":"The generalized maximal operator on measures","authors":"J. Bonazza,&nbsp;M. Carena,&nbsp;M. Toschi","doi":"10.1007/s10476-025-00066-9","DOIUrl":"10.1007/s10476-025-00066-9","url":null,"abstract":"<div><p>In this article we present the definition of the generalized maximal operator <span>(M_Phi)</span> acting on measures and we prove some of its basic properties. More precisely, we demonstrate that <span>(M_Phi)</span> satisfies a Kolmogorov inequality and that this operator is of weak type <span>((1,1))</span>. This allow us to obtain a family of <span>(A_p)</span> weights involving the distance <span>(d(x,F))</span> to a closed set <span>(F)</span> in a framework of Ahlfors spaces. Also, we prove that <span>(M_Phi)</span> satisfies a weighted modular weak type inequality associated to the Young function <span>(Phi)</span>, and we give another one that yields a sufficient condition for the weight to belong to the <span>(A_1)</span> class.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"75 - 97"},"PeriodicalIF":0.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00066-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-posedness of linear singular evolution equations in Banach spaces: theoretical results Banach空间中线性奇异演化方程的适定性：理论结果
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2025-03-06 DOI: 10.1007/s10476-025-00067-8
M. C. Bortolan, M. C. A. Brito, F. Dantas
{"title":"Well-posedness of linear singular evolution equations in Banach spaces: theoretical results","authors":"M. C. Bortolan,&nbsp;M. C. A. Brito,&nbsp;F. Dantas","doi":"10.1007/s10476-025-00067-8","DOIUrl":"10.1007/s10476-025-00067-8","url":null,"abstract":"<div><p>In this work we deal with a <i>singular</i> evolution equation of the form\u0000</p><div><div><span>$$begin{cases}Edot{u} = Au, &amp;t&gt;0, u(0)=u_0,end{cases}$$</span></div></div><p>\u0000where both <span>(A)</span> and <span>(E)</span> are linear operators, with <span>(E)</span> bounded but <i>not necessarily injective</i>, defined in adequate subspaces of a given Banach space <span>(X)</span>. By using the concept of <i>generalized semigroups</i>, our goal is to prove a Hille-Yosida type theorem for this problem, that is, to find necessary and sufficient conditions under which <span>(A)</span> is the generator of a generalized semigroup <span>({U(t) : t geq 0})</span>. This problem is dealt with by making use of the <span>(E)</span>-<i>spectral theory</i> and the concept of <i>generalized integrable families</i>. Finally, we present an abstract example that illustrates the theory. \u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"99 - 128"},"PeriodicalIF":0.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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