Analysis Mathematica最新文献

{"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}

{"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}

{"title":"Boundedness properties of modified averaging operators and geometrically doubling metric spaces","authors":"J. M. Aldaz,&nbsp;A. Caldera","doi":"10.1007/s10476-025-00068-7","DOIUrl":"10.1007/s10476-025-00068-7","url":null,"abstract":"<div><p>We characterize the geometrically doubling condition of a metric space in terms of the uniform <span>(L^1)</span>-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"23 - 33"},"PeriodicalIF":0.6,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00068-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707142","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}

{"title":"On the existence of an extremal function for the Delsarte extremal problem","authors":"M. D. Ramabulana","doi":"10.1007/s10476-025-00072-x","DOIUrl":"10.1007/s10476-025-00072-x","url":null,"abstract":"<div><p>In the general setting of a locally compact Abelian group <i>G</i>, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions <span>(f colon G to mathbb{R})</span> satisfying <span>(f(0) = 1)</span> and having <span>(supp f_{+} subset Omega)</span> for some measurable subset <span>(Omega)</span> of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when <span>(Omega)</span> is closed, extending previously known existence results to a larger class of functions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"279 - 291"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00072-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707098","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}

{"title":"The Bishop-Phelps-Bollobás property for operators defined on (c_0)-sum of Euclidean spaces","authors":"T. Grando,&nbsp;M. L. Lourenço","doi":"10.1007/s10476-025-00070-z","DOIUrl":"10.1007/s10476-025-00070-z","url":null,"abstract":"<div><p>The main purpose of this paper is to study the Bishop-Phelps-Bollobás property for operators on <span>(c_0)</span>-sum of Euclidean spaces. We show that the pair <span>( (c_0(bigoplus^{infty}_{k=1}ell^{k}_{2} ),Y))</span> has\u0000 the Bishop-Phelps-Bollobás property for operators (shortly BPBp for operators) whenever <span>(Y)</span> is a uniformly convex Banach space.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"211 - 224"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707100","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}

{"title":"Inequalities for (1/(1-cos(x) )) and its derivatives","authors":"H. Alzer,&nbsp;H. L. Pedersen","doi":"10.1007/s10476-025-00069-6","DOIUrl":"10.1007/s10476-025-00069-6","url":null,"abstract":"<div><p>We prove that the function <span>(g(x)= 1 / ( 1 - cos(x) ))</span> is completely monotonic on <span>((0,pi])</span> and absolutely monotonic on <span>([pi, 2pi))</span>, and we determine the best possible bounds <span>(lambda_n)</span> and <span>(mu_n)</span> such that the inequalities\u0000</p><div><div><span>$$\u0000lambda_n leq g^{(n)}(x)+g^{(n)}(y)-g^{(n)}(x+y) quad (n geq 0 mbox{even})\u0000$$</span></div></div><p>\u0000and\u0000</p><div><div><span>$$\u0000mu_n leq g^{(n)}(x+y)-g^{(n)}(x)-g^{(n)}(y) quad (n geq 1 mbox{odd})\u0000$$</span></div></div><p>\u0000hold for all <span>(x,yin (0,pi))</span> with <span>(x+yleq pi)</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"63 - 73"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00069-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707101","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}

{"title":"Properties of solutions of the (alpha)-harmonic equation in the unit disk","authors":"Z. Y. Hu,&nbsp;J. H. Fan,&nbsp;H. M. Srivastava","doi":"10.1007/s10476-025-00071-y","DOIUrl":"10.1007/s10476-025-00071-y","url":null,"abstract":"<div><p>In this paper, we study Riesz-Fejér inequality, comparative growth of integral means and boundary behavior for solutions of the <span>(alpha)</span>-harmonic equation in the unit disk <span>(mathbb{D})</span>. For <span>(alpha&gt;max{-1,-frac{2}{p}})</span> \u0000<span>(alpha geq 0)</span> \u0000and <span>(1&lt;p&lt;infty)</span>, we obtain a Riesz-Fejér inequality for functions in the real kernel <span>(alpha)</span>-harmonic Hardy space consisting of solutions <span>(u)</span> of the <span>(alpha)</span>-harmonic equation in <span>(mathbb{D})</span> with uniformly bounded integral mean <span>(M_{p}(r, u))</span> with respect to <span>(rin(0,1))</span>. Furthermore, for <span>(1leq p&lt;qleqinfty)</span>, we estimate the growth of <span>(M_{q}(r,u))</span> if the growth of <span>(M_{p}(r,u))</span> is known. Moreover, we consider the boundary behavior of real kernel <span>(alpha)</span>-Poisson integrals in <span>(mathbb{D})</span>, where <span>(alpha&gt;-1)</span>. Our results generalize the related previous results.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"225 - 240"},"PeriodicalIF":0.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707099","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}

{"title":"Bohr phenomenon for harmonic Bloch functions","authors":"V. Allu,&nbsp;H. Halder","doi":"10.1007/s10476-025-00063-y","DOIUrl":"10.1007/s10476-025-00063-y","url":null,"abstract":"<div><p>\u0000For <span>(alpha in (0,infty))</span>, let \u0000<span>(mathcal{B}_{mathcal{H},Omega}(alpha))</span> denote the class of <span>(alpha)</span>-Bloch mappings on a proper simply connected domain <span>(Omega subseteq mathbb{C})</span>. \u0000In this article, we introduce the class <span>(mathcal{B}^{*}_{mathcal{H},Omega}(alpha))</span> of harmonic <span>(alpha)</span>-Bloch-type mappings on a proper simply connected domain <span>(Omega subseteq mathbb{C})</span> and study several interesting properties of the classes <span>(mathcal{B}_{mathcal{H},Omega}(alpha))</span> and <span>(mathcal{B}^{*}_{mathcal{H},Omega}(alpha))</span> when <span>(Omega)</span> is proper simply connected domain and the shifted disk <span>(Omega_{gamma})</span> containing <span>(mathbb{D})</span>, where \u0000</p><div><div><span>$$Omega_{gamma}:=big{zinmathbb{C} : big|z+frac{gamma}{1-gamma}big|&lt;frac{1}{1-gamma}big}$$</span></div></div><p> and <span>(0 leq gamma &lt;1)</span>. For <span>(f in mathcal{B}_{mathcal{H},Omega}(alpha))</span> (respectively <span>(mathcal{B}^{*}_{mathcal{H},Omega}(alpha)))</span> of the form <span>(f(z)=h(z) + overline{g(z)}=sum_{n=0}^{infty}a_nz^n + overline{sum_{n=1}^{infty}b_nz^n})</span> in <span>(mathbb{D})</span> with Bloch norm <span>( lVert f rVert _{mathcal{H},Omega, alpha} leq 1)</span> (respectively \u0000<span>( lVert f rVert ^{*}_{mathcal{H},Omega, alpha} leq 1)</span>), we define the Bloch–Bohr radius for the class <span>(mathcal{B}_{mathcal{H},Omega}(alpha))</span> (respectively \u0000<span>(mathcal{B}^{*}_{mathcal{H},Omega}(alpha)))</span> to be the largest radius \u0000<span>(r_{Omega,alpha} in (0,1))</span> such that <span>(sum_{n=0}^{infty}(|a_n|+|b_{n}|) r^nleq 1)</span> for \u0000<span>(r leq r_{Omega, alpha})</span> and for all <span>(f in mathcal{B}_{mathcal{H},Omega}(alpha))</span> (respectively <span>(mathcal{B}^{*}_{mathcal{H},Omega}(alpha)))</span>. We also investigate Bloch–Bohr radius for the classes <span>(mathcal{B}_{mathcal{H},Omega}(alpha))</span> and <span>(mathcal{B}^{*}_{mathcal{H},Omega}(alpha))</span> on simply connected domain <span>(Omega)</span> containing \u0000<span>(mathbb{D})</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"35 - 62"},"PeriodicalIF":0.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00063-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707164","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}

{"title":"Finiteness of meromorphic mappings sharing (2n) hyperplanes in (mathbb P^n(mathbb C)) with truncated multiplicities","authors":"H. T. Thuy,&nbsp;P. D. Thoan,&nbsp;N. T. Nhung","doi":"10.1007/s10476-025-00064-x","DOIUrl":"10.1007/s10476-025-00064-x","url":null,"abstract":"<div><p>In this paper, we give a result on finiteness of meromorphic mappings from <span>(mathbb C^m)</span> into <span>(mathbb P^n(mathbb C))</span> sharing hyperplanes in general position with truncated multiplicities to level <span>(n)</span>. In our result, the number of shared hyperplanes is just <span>(2n)</span> instead of <span>(2n+1)</span> or <span>(2n+2)</span> as in the previous results, but the number of involving meromorphic mappings still does not exceed 2.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"293 - 322"},"PeriodicalIF":0.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707163","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}

{"title":"Characterization for boundedness of some commutators of the multilinear fractional Calderón–Zygmund operators with Dini type kernel","authors":"W. Zhao,&nbsp;J. Wu","doi":"10.1007/s10476-025-00065-w","DOIUrl":"10.1007/s10476-025-00065-w","url":null,"abstract":"<div><p>Let <span>(T_{alpha})</span> be an <span>(m)</span>-linear fractional Calderón–Zygmund operator with kernel of mild regularity, and <span>(vec{b} =(b_{1},b_{2} ,ldots,b_{m}))</span> be a collection of locally integrable functions. In this paper, the main purpose is to establish some estimates for the mapping property of the multilinear commutators <span>( T_{{alpha,Sigma vec{b}}})</span> in the context of the variable exponent function spaces. The key tools used are the Fourier series and the pointwise estimates involving the sharp maximal operator of the multilinear commutator and certain associated maximal operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"323 - 362"},"PeriodicalIF":0.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143707162","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}