{"title":"A necessary condition for the boundedness of the maximal operator on (L^{p(cdot)}) over reverse doubling spaces of homogeneous type","authors":"O. Karlovych, A. Shalukhina","doi":"10.1007/s10476-024-00053-6","DOIUrl":"10.1007/s10476-024-00053-6","url":null,"abstract":"<div><p>Let <span>((X,d,mu))</span> be a space of homogeneous type and <span>(p(cdot) colon X to[1,infty])</span> be a variable exponent. We show that if the measure <span>(mu)</span> is Borel-semiregular and reverse doubling, then the condition \u0000<span>({ess,inf}_{xin X}p(x)>1)</span> \u0000is necessary for the boundedness of the Hardy–Littlewood maximal operator <span>(M)</span> \u0000on the variable Lebesgue space <span>(L^{p(cdot)}(X,d,mu))</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"241 - 248"},"PeriodicalIF":0.6,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00053-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143706885","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":"Curves in the Fourier zeros of polytopal regions and the Pompeiu problem","authors":"M. N. Kolountzakis, E. Spyridakis","doi":"10.1007/s10476-024-00054-5","DOIUrl":"10.1007/s10476-024-00054-5","url":null,"abstract":"<div><p>We prove that any finite union <i>P</i> of interior-disjoint polytopes in <span>(mathbb R^d)</span> has the Pompeiu property, a result first proved by Williams \u0000[15]. This means that if a continuous function <i>f</i> on <span>(mathbb R^d)</span> integrates to 0 on any congruent copy of <span>(P)</span> then <span>(f)</span> is identically 0. By a fundamental result of Brown, Schreiber and Taylor \u0000[4], this is equivalent to showing that the Fourier–Laplace transform of the indicator function of <i>P</i> does not vanish identically on any 0-centered complex sphere in <span>(mathbb C^d)</span>. Our proof initially follows the recent one of Machado and Robins \u0000[12] who are using the Brion–Barvinok formula for the Fourier–Laplace transform of a polytope. But we simplify this method considerably by removing the use of properties of Bessel function zeros. Instead we use some elementary arguments on the growth of linear combinations of exponentials with rational functions as coefficients. Our approach allows us to prove the non-existence of complex spheres of any center in the zero-set of the Fourier–Laplace transform. The planar case is even simpler in that we do not even need the Brion–Barvinok formula. We then go further in the question of which sets can be contained in the null set of the Fourier–Laplace transform of a polytope by extending results of Engel \u0000[7] who showed that rationally parametrized hypersurfaces, under some mild conditions, cannot be contained in this null-set. We show that a rationally parametrized <i>curve</i> which is not contained in an affine hyperplane in <span>(mathbb C^d)</span> cannot be contained in this null-set. Results about curves parametrized by meromorphic functions are also given.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 4","pages":"1081 - 1098"},"PeriodicalIF":0.6,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859503","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":"Approximation by a special de la Vallée Poussin type matrix transform mean of Vilenkin–Fourier series","authors":"I. Blahota, D. Nagy","doi":"10.1007/s10476-024-00049-2","DOIUrl":"10.1007/s10476-024-00049-2","url":null,"abstract":"<div><p>We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system. \u0000We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of \u0000continuity of the function. We also give theorems with respect to norm and almost everywhere convergences.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"939 - 957"},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264977","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":"Value cross-sharing problems on meromorphic functions","authors":"Y. C. Gao, K. Liu, F. N. Wang","doi":"10.1007/s10476-024-00051-8","DOIUrl":"10.1007/s10476-024-00051-8","url":null,"abstract":"<div><p>In this paper, we continue to consider the value cross-sharing problems on meromorphic functions. We mainly present some results and improvements on <span>(f(z))</span> and <span>(g(z))</span> provided that <span>(f(z))</span> and <span>(g^{(k)}(z))</span> share common values together with <span>(g(z))</span> and <span>(f^{(k)}(z))</span> share the same or different common values CM or IM, where <span>(f(z), g(z))</span> are meromorphic functions and <span>(k)</span> is a positive integer. With additional conditions on deficiency, we get more accurate relations on <span>(f(z))</span> and <span>(g(z))</span> when <span>(f(z))</span> and <span>(g^{(k)}(z))</span> share a CM together with <span>(g(z))</span> and <span>(f^{(k)}(z))</span> share <i>b</i> CM, where <i>a</i>, <i>b</i> are constants.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"191 - 209"},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00051-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264975","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":"Large dilates of hypercube graphs in the plane","authors":"V. Kovač, B. Predojević","doi":"10.1007/s10476-024-00045-6","DOIUrl":"10.1007/s10476-024-00045-6","url":null,"abstract":"<div><p>We study a distance graph <span>(Gamma_n)</span> that is isomorphic to the <span>(1)</span>-skeleton of an <span>(n)</span>-dimensional unit hypercube. We show that every measurable set of positive upper Banach density in the plane contains all sufficiently large dilates of <span>(Gamma_n)</span>. This provides the first examples of distance graphs other than the trees for which a dimensionally sharp embedding in positive density sets is known.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"893 - 915"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264970","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":"Decomposable operators acting between distinct (L^p)-direct integrals of Banach spaces","authors":"N. Evseev, A. Menovschikov","doi":"10.1007/s10476-024-00044-7","DOIUrl":"10.1007/s10476-024-00044-7","url":null,"abstract":"<div><p>The notion of decomposable operators acting between distinct <span>(L^p)</span>-direct \u0000integrals of Banach spaces is introduced. We show that these operators generalize the composition operator in the sense that a binary relation replaces a \u0000mapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"861 - 892"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264971","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":"On the inequalities of Zygmund and de Bruijn","authors":"R. R. Akopyan, P. Kumar, G. V. Milovanović","doi":"10.1007/s10476-024-00048-3","DOIUrl":"10.1007/s10476-024-00048-3","url":null,"abstract":"<div><p>For the polar derivative <span>(D_alpha P(z) =nP(z)+(alpha-z)P'(z))</span> of \u0000a polynomial <span>(P(z))</span> of degree <i>n</i>, most of \u0000the <span>(L^p)</span> inequalities available in the literature are for restricted values of <span>(alpha)</span>, and in this \u0000paper we extend few such fundamental results to all of <span>(alpha)</span> in the complex plane.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 4","pages":"967 - 986"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264973","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":"An asymptotic equality of Cartan's Second Main Theorem and some generalizations","authors":"Y. Chen","doi":"10.1007/s10476-024-00043-8","DOIUrl":"10.1007/s10476-024-00043-8","url":null,"abstract":"<div><p>Motivated by [19] and [10], we define the modified proximity function <span>(overline{m}_{q}(f,r))</span> \u0000for entire curves in complex projective space <span>(mathbf{P}^nmathbf{C})</span>, and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of \u0000[19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"129 - 163"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264976","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}
L. Abadias, J. E. Galé, P. J. Miana, J. Oliva-Maza
{"title":"On the hyperbolic group and subordinated integrals as operators on sequence Banach spaces","authors":"L. Abadias, J. E. Galé, P. J. Miana, J. Oliva-Maza","doi":"10.1007/s10476-024-00047-4","DOIUrl":"10.1007/s10476-024-00047-4","url":null,"abstract":"<div><p>We show that the composition hyperbolic group in the unit disc, once transferred to act on sequence spaces, is bounded on <span>(ell^p)</span> if and only if <span>({p=2})</span>. We introduce some integral operators subordinated to that group which are natural generalizations of classical operators on sequences. For the description of such operators, we use some combinatorial identities which look interesting in their own.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 1","pages":"1 - 22"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00047-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264974","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 strong extension groups of Cuntz–Krieger algebras","authors":"K. Matsumoto","doi":"10.1007/s10476-024-00046-5","DOIUrl":"10.1007/s10476-024-00046-5","url":null,"abstract":"<div><p>In this paper, we study the strong extension groups of Cuntz–Krieger algebras, and present a formula to compute the groups. We also detect the position of the Toeplitz extension of a Cuntz–Krieger algebra in the strong extension group and in the weak extension group to see that the weak extension group with the position of the Toeplitz extension is a complete invariant of the isomorphism class of the Cuntz–Krieger algebra associated with its transposed matrix.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"917 - 937"},"PeriodicalIF":0.6,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269197","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}