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A generalized radial integration by parts formula and its applications to Caffarelli–Kohn–Nirenberg inequalities 广义径向分部积分公式及其在Caffarelli-Kohn-Nirenberg不等式中的应用
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-26 DOI: 10.1007/s13324-025-01060-y
Giovanni Di Fratta, Alberto Fiorenza
{"title":"A generalized radial integration by parts formula and its applications to Caffarelli–Kohn–Nirenberg inequalities","authors":"Giovanni Di Fratta,&nbsp;Alberto Fiorenza","doi":"10.1007/s13324-025-01060-y","DOIUrl":"10.1007/s13324-025-01060-y","url":null,"abstract":"<div><p>This paper builds upon the Caffarelli–Kohn–Nirenberg (CKN) weighted interpolation inequalities, which are fundamental tools in partial differential equations and geometric analysis for establishing relationships between functions and their gradients when power weights are involved. Our work broadens the scope of these inequalities by generalizing them to encompass a broader class of radial weights and exponents. Additionally, we extend the application of these inequalities to the class <span>(C^{infty } ( {overline{Omega }}))</span> of smooth functions defined on bounded domains with Lipschitz boundaries. To achieve this generalization, we formulate a new integration by parts formula that accounts for more general weights, a wider range of exponents, and <span>(C^{infty }({overline{Omega }}))</span> functions. The resulting generalized CKN-type inequalities offer explicit upper bounds on the optimal constants, independent of the domain’s geometry, consistent with the scaling invariant nature of the inequalities.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01060-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875296","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
Stretch maps on the affine-additive group 仿射加性群上的拉伸映射
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1007/s13324-025-01047-9
Zoltán M. Balogh, Elia Bubani, Ioannis D. Platis
{"title":"Stretch maps on the affine-additive group","authors":"Zoltán M. Balogh,&nbsp;Elia Bubani,&nbsp;Ioannis D. Platis","doi":"10.1007/s13324-025-01047-9","DOIUrl":"10.1007/s13324-025-01047-9","url":null,"abstract":"<div><p>We define linear and radial stretch maps in the affine-additive group, and prove that they are minimizers of the mean quasiconformal distortion functional. For the proofs we use a method based on the notion of modulus of a curve family and the minimal stretching property (MSP) of the afore-mentioned maps. MSP relies on certain given curve families compatible with the respective geometric settings of the stretch maps.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01047-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875449","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
Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds 幂零李群及其紧零流形上的半经典泛函微积分
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-24 DOI: 10.1007/s13324-025-01051-z
Véronique Fischer, Søren Mikkelsen
{"title":"Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds","authors":"Véronique Fischer,&nbsp;Søren Mikkelsen","doi":"10.1007/s13324-025-01051-z","DOIUrl":"10.1007/s13324-025-01051-z","url":null,"abstract":"<div><p>In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these operators are sub-Laplacians in horizontal divergence form perturbed with a potential and their generalisations.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01051-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871372","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
An analogue of Koebe’s theorem and the openness of a limit map in one class 科贝定理的类比和一类极限映射的开放性
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-24 DOI: 10.1007/s13324-025-01058-6
Evgeny Sevost’yanov, Valery Targonskii
{"title":"An analogue of Koebe’s theorem and the openness of a limit map in one class","authors":"Evgeny Sevost’yanov,&nbsp;Valery Targonskii","doi":"10.1007/s13324-025-01058-6","DOIUrl":"10.1007/s13324-025-01058-6","url":null,"abstract":"<div><p>We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class. This statement can be interpreted as the well-known analogue of Koebe’s theorem for analytic functions. As an application of the obtained result, we show that, if a sequence of mappings belonging to the specified class converges locally uniformly, then the limit mapping is open.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871175","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
Criteria for boundedness of a class of integral operators from (L_p) to (L_q) for (1 一类从(L_p)到(L_q)的积分算子的有界性准则 (1<q<p<infty )
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-22 DOI: 10.1007/s13324-025-01053-x
Ryskul Oinarov, Ainur Temirkhanova, Aigerim Kalybay
{"title":"Criteria for boundedness of a class of integral operators from (L_p) to (L_q) for (1<q<p<infty )","authors":"Ryskul Oinarov,&nbsp;Ainur Temirkhanova,&nbsp;Aigerim Kalybay","doi":"10.1007/s13324-025-01053-x","DOIUrl":"10.1007/s13324-025-01053-x","url":null,"abstract":"<div><p>In this paper, we consider integral operators with non-negative kernels that satisfy conditions less restrictive than those studied earlier. We establish criteria for the boundedness of these operators in Lebesgue spaces.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143861388","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
Fixed points theorems via the degree of nondensifiability with an application to nonlinear hybrid fractional integral inclusions 不动点定理在非线性混合分数阶积分内含物中的应用
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-20 DOI: 10.1007/s13324-025-01056-8
Khaled Ben Amara, Aref Jeribi, Najib Kaddachi
{"title":"Fixed points theorems via the degree of nondensifiability with an application to nonlinear hybrid fractional integral inclusions","authors":"Khaled Ben Amara,&nbsp;Aref Jeribi,&nbsp;Najib Kaddachi","doi":"10.1007/s13324-025-01056-8","DOIUrl":"10.1007/s13324-025-01056-8","url":null,"abstract":"<div><p>Invoking the concept of <span>(alpha )</span>-dense curves, we develop a new fixed point approach for multi-valued mappings which works under more general conditions than Darbo multi-valued fixed point theorem and its generalizations. We prove some generalizations of Krasnosielskii’s type fixed point theorems and we establish nonlinear alternatives of Leray-Schauder’s type for multi-valued mappings. This theory is then applied to investigate general existence principles of nonlinear hybrid fractional integral inclusions in abstract Banach spaces. Our results extend and generalize a number of earlier works.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871396","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 behavior of (m-th) derivatives of polynomials in bounded and unbounded regions without zero angles in weighted Lebesgue spaces 论加权勒贝格空间有界和无界区域中无零角多项式的（m-th）导数的行为
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-18 DOI: 10.1007/s13324-025-01055-9
F. G. Abdullayev, M. Imashkyzy
{"title":"On the behavior of (m-th) derivatives of polynomials in bounded and unbounded regions without zero angles in weighted Lebesgue spaces","authors":"F. G. Abdullayev,&nbsp;M. Imashkyzy","doi":"10.1007/s13324-025-01055-9","DOIUrl":"10.1007/s13324-025-01055-9","url":null,"abstract":"<div><p>In this paper, we study the growth of the <span>(m-th)</span> (<span>(mge 1)</span>) derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces over the whole complex plane. We first study the growth of the <span>(m-th)</span> derivatives of an arbitrary algebraic polynomial over unbounded regions of the complex plane, and then we obtain estimates for the growth of the <span>(m-th)</span> derivatives of this polynomial over the closure of the given region. Combining both estimates, we find estimates for the growth of the <span>(m-th)</span> derivatives of an arbitrary algebraic polynomial over the whole complex plane.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01055-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143849002","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
On Schrödinger semigroups generated by universal Malliavin calculus 关于广义Malliavin微积分生成的Schrödinger半群
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-17 DOI: 10.1007/s13324-025-01054-w
Oleh Lopushansky
{"title":"On Schrödinger semigroups generated by universal Malliavin calculus","authors":"Oleh Lopushansky","doi":"10.1007/s13324-025-01054-w","DOIUrl":"10.1007/s13324-025-01054-w","url":null,"abstract":"<div><p>Using Malliavin’s calculus, it is proved that the generator of the one-parameter unitary semigroup of Schrödinger type on the complex Hilbert space <span>(L^2_mathbb {C}(mathbb {R}^n,gamma ))</span> equipped with the Gaussian measure <span>(gamma )</span> on <span>(mathbb {R}^n)</span> takes the form <span>(sum _j^n(mathfrak {h}_2(phi _{jmath })+1))</span>, where <span>(mathfrak {h}_2(phi _{jmath }))</span> are second-order Hermite polynomials of independent random variables <span>(phi _jmath )</span>, generated by an orthonormal basis in <span>(mathbb {R}^n)</span> using the Paley-Wiener maps. The Weyl-Schrödinger unitary irreducible representation of Heisenberg matrix group <span>(mathbb {H}_{2n+1})</span> and the Segal-Bargmann transform are essentially used. By applying the inverse Gauss transform, it is found that this representation of <span>(mathbb {H}_{2n+1})</span> can be fully described by complex Weyl pairs, generated using the multiplication operator with a real Gaussian variable on <span>(mathbb {R}^n)</span>.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143845734","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
Kleinecke–Shirokov theorem: a version for isometric transformations 克莱涅克-希罗科夫定理：等距变换的版本
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-13 DOI: 10.1007/s13324-025-01057-7
Hranislav Stanković
{"title":"Kleinecke–Shirokov theorem: a version for isometric transformations","authors":"Hranislav Stanković","doi":"10.1007/s13324-025-01057-7","DOIUrl":"10.1007/s13324-025-01057-7","url":null,"abstract":"<div><p>In this paper, we present a version of the Kleinecke–Shirokov Theorem applicable to isometries on a Hilbert space <span>({mathcal {H}})</span>. Specifically, we demonstrate that if <span>( V in {mathfrak {B}}({mathcal {H}}))</span> is a quasinormal partial isometry and <span>(T in {mathfrak {B}}({mathcal {H}}))</span> satisfies <span>({mathcal {R}}(T) subseteq {mathcal {R}}(V))</span>, then </p><div><div><span>$$begin{aligned} [V,[V,T]]=0quad implies quad [V,T]=0. end{aligned}$$</span></div></div><p>We also consider the mixed commutators of two isometries, and their belonging to the Schatten-von Neumann classes. Finally, we show that the corresponding classical statement regarding normal operators can be derived from our results.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824617","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
Representation of real interpolation spaces using weighted couples of radon measures 用radon测度的加权偶表示实插值空间
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-04-10 DOI: 10.1007/s13324-025-01050-0
Per G. Nilsson
{"title":"Representation of real interpolation spaces using weighted couples of radon measures","authors":"Per G. Nilsson","doi":"10.1007/s13324-025-01050-0","DOIUrl":"10.1007/s13324-025-01050-0","url":null,"abstract":"<div><p>Using couples of weighted Radon measures an extension of the J-method of interpolation is described. This method allows for the representation also of non-regular interpolation spaces. In particular, Banach couples with the Calderon–Mitjagin property has all its interpolation spaces described by this extension.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818213","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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