Acta Mathematica Hungarica最新文献

{"title":"On (F)-spaces of almost-Lebesgue functions","authors":"N. J. Alves","doi":"10.1007/s10474-025-01552-0","DOIUrl":"10.1007/s10474-025-01552-0","url":null,"abstract":"<div><p>We consider the space of functions almost in <span>(L_p)</span> and endow it with the topology of asymptotic <span>(L_p)</span>-convergence. This yields a completely metrizable topological vector space which, on finite measure spaces, coincides with the space of measurable functions equipped with the topology of (local) convergence in measure. We investigate analogs of classical results such as dominated convergence and Vitali convergence theorems. For <span>(mathbb{R}^d)</span> as the underlying measure space, we establish results on approximation by smooth functions and separability. Further aspects, including local boundedness, local convexity, and duality are examined in the <span>(mathbb{R}^d)</span> setting, revealing fundamental differences from standard <span>(L_p)</span> spaces.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"365 - 386"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01552-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230394","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 open-separated sequences","authors":"A. Bella,&nbsp;N. Carlson,&nbsp;S. Spadaro,&nbsp;P. Szeptycki","doi":"10.1007/s10474-025-01553-z","DOIUrl":"10.1007/s10474-025-01553-z","url":null,"abstract":"<div><p>\u0000We introduce the notion of an open-separated sequence, related to a free sequence, and define the cardinal function\u0000<span>(text{os} ( X))</span>. Nonregular and regular examples <span>(X)</span> are given such that <span>(text{os} ( X)&lt;F(X))</span>. Motivated by a question of Angelo Bella, we show that if\u0000<span>(X)</span> is Hausdorff then <span>(|X|leq hL(X)^{text{os} ( X)psi_c(X)})</span>. As\u0000<span>(text{os} ( X)psi_c(X)leq hL(X))</span> if <span>(X)</span> is Hausdorff, this gives a\u0000strengthening of the De Groot-Smirnov bound <span>(2^{hL(X)})</span> for the\u0000cardinality of a Hausdorff space. Additionally we show <span>( text{nw}( X)leq text{hL}(X)^{text {os} ( X)})</span> if <span>(X)</span> is regular. A consequence is that if <span>(X)</span> is regular and either almost radial or hereditarily weakly Whyburn then <span>( { |X|leq hL(X)^{text{os} ( X)} } )</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"387 - 399"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01553-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230396","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":"Rotational beta expansions and Schmidt games","authors":"J. Caalim,&nbsp;H. Kaneko,&nbsp;N. Nollen","doi":"10.1007/s10474-025-01555-x","DOIUrl":"10.1007/s10474-025-01555-x","url":null,"abstract":"<div><p>\u0000We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively.\u0000We give sufficient conditions on the parameters <span>(alpha, beta in (0,1))</span> so that particular cylinder sets arising from the expansions are winning or losing Schmidt <span>((alpha,beta))</span>-game.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"400 - 436"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230451","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":"Olsen's inequality for discrete Morrey spaces","authors":"H. Gunawan,&nbsp;Y. Ramadana,&nbsp;Y. Sawano","doi":"10.1007/s10474-025-01557-9","DOIUrl":"10.1007/s10474-025-01557-9","url":null,"abstract":"<div><p>\u0000The aim of this paper is to establish the Olsen's inequality for discrete Morrey spaces. Specifically, it focuses on a bilinear operator associated with the discrete fractional integral operator of order <span>(alpha)</span> within these spaces. To achieve this, the decomposition method for discrete Morrey spaces is thoroughly examined.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"447 - 456"},"PeriodicalIF":0.6,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230414","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 some hereditary and super classes of directly finite Abelian groups","authors":"P. Danchev,&nbsp;B. Goldsmith,&nbsp;F. Karimi","doi":"10.1007/s10474-025-01546-y","DOIUrl":"10.1007/s10474-025-01546-y","url":null,"abstract":"<div><p>Continuing recent studies of both the hereditary and super properties of certain classes of Abelian groups, we explore in-depth what is the situation in the quite large class consisting of directly finite Abelian groups.</p><p>Trying to connect some of these classes, we specifically succeeded to prove the surprising criteria that a relatively Hopfian group is hereditarily Hopfian only when it is extended Bassian, as well as that, a relatively Hopfian group is super Hopfian only when it is extended Bassian. In this aspect, additional relevant necessary and sufficient conditions in a slightly more general context are also proved.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"457 - 472"},"PeriodicalIF":0.6,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01546-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230235","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":"An approximation form of the Kuratowski Extension Theorem for Baire-alpha functions","authors":"W. Sieg","doi":"10.1007/s10474-025-01550-2","DOIUrl":"10.1007/s10474-025-01550-2","url":null,"abstract":"<div><p>Let <span>(Omega)</span> be a perfectly normal topological space, let <span>(A)</span> be a non-empty <span>(G_delta)</span>-subset of <span>(Omega)</span> and let <span>(mathscr{B}_1(A))</span> denote the space of all functions <span>(Atomathbb {R})</span> of Baire-one class on <span>(A)</span>.\u0000Let also <span>(|cdot|_infty)</span> be the supremum norm. The symbol <span>(chi_A)</span> stands for the characteristic function of <span>(A)</span>. We prove that for every bounded function <span>(finmathscr {B}_1(A))</span> there is a sequence <span>((H_n))</span>\u0000of both <span>(F_sigma)</span>- and <span>(G_delta)</span>-subset of <span>(Omega)</span> such that the function <span>(overline{f}colonOmegatomathbb {R})</span> given by the uniformly convergent series on <span>(Omega)</span> with the formula:\u0000<span>( overline{f}:=csum_{n=0}^infty (frac{2}{3})^{n+1}(frac{1}{2}-chi_{H_n}) )</span>\u0000extends <span>(f)</span> with <span>(overline{f}in{mathscr{B}}_1(Omega))</span>, <span>(c=sup_{xinOmega}lvert{overline{f}(x)}rvert)</span> and the condition <span>((triangle))</span> of the form:\u0000<span>(|f|_infty=|overline{f}|_infty)</span>.\u0000We apply the above series to obtain an extension of <span>(f)</span> positive to <span>(overline{f})</span> positive with the condition <span>((triangle))</span>. A similar technique allows us to obtain an extension of Baire-alpha function\u0000on <span>(A)</span> to Baire-alpha function on <span>(Omega)</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"313 - 320"},"PeriodicalIF":0.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01550-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230333","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 number of vertices/edges whose deletion preserves the Kőnig–Egerváry property","authors":"V. E. Levit,&nbsp;E. Mandrescu","doi":"10.1007/s10474-025-01549-9","DOIUrl":"10.1007/s10474-025-01549-9","url":null,"abstract":"<div><p>Let <span>(alpha(G))</span>\u0000 and <span>(mu(G))</span>\u0000 denote the cardinality of a maximum independent\u0000set and the size of a maximum matching, respectively, in the graph <span>(G= (V,E) )</span>\u0000. If <span>(alpha(G)+mu(G)= lvert V rvert )</span>\u0000, then <i>G</i> is a\u0000Kőnig–Egerváry graph.</p><p>The number <span>(d (G) =max{ lvert A rvert - lvert N (A) rvert :Asubseteq V})</span> is the critical\u0000difference of the graph <i>G</i>, where <span>(N (A) =left{ v:vin V,N (v) cap Aneqemptysetright} )</span>\u0000. Every set <span>(Bsubseteq V)</span>\u0000satisfying <span>(d (G) = lvert B rvert - lvert N (B) rvert )</span>\u0000 is <i>critical</i>. Let <span>(varepsilon (G) = lvert mathrm{ker}(G) rvert )</span>\u0000 and <span>(xi (G) = lvert mathrm{core} (G) rvert )</span>\u0000, where <span>(mathrm{ker}(G))</span>\u0000 is the intersection of all critical independent sets, and <span>( mathrm{core} (G) )</span>\u0000 is the intersection of all maximum independent sets. It\u0000is known that <span>(mathrm{ker}(G)subseteq)</span>\u0000 <span>( mathrm{core} (G) )</span>\u0000holds for every graph.</p><p>Let us define\u0000</p><ul>\u0000 <li>\u0000 <p><span>(varrho_{v} (G) = lvert { vin V:G-v )</span> is a Kőnig–Egerváry graph <span>(} rvert )</span>;</p>\u0000 </li>\u0000 <li>\u0000 <p><span>(varrho_{e} (G) = lvert { ein E:G-e )</span> is a Kőnig–Egerváry graph <span>( } rvert )</span>.</p>\u0000 </li>\u0000 </ul><p>Clearly, <span>(varrho_{v} (G) = lvert V rvert )</span> and\u0000<span>(varrho_{e} (G) = lvert E rvert )</span> for bipartite graphs.\u0000Unlike the bipartiteness, the property of being a Kőnig–Egerváry graph\u0000is not hereditary.</p><p>In this paper, we show that\u0000</p><div><div><span>$$varrho_{v} (G) = lvert V rvert -xi (G) +varepsilon (G)phantom{a} phantom{a}text{and}phantom{a} phantom{a} varrho_{e} (G) geq lvert E rvert -xi (G) +varepsilon (G)$$</span></div></div><p> for every Kőnig–Egerváry graph <i>G</i>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"321 - 340"},"PeriodicalIF":0.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230540","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":"A linear independence criterion for certain infinite series with polynomial orders","authors":"S. Kudo","doi":"10.1007/s10474-025-01548-w","DOIUrl":"10.1007/s10474-025-01548-w","url":null,"abstract":"<div><p>Let <i>q</i> be a Pisot or Salem number. Let <span>(f_j(x) quad (j=1,2,dots))</span> be integer-valued polynomials of degree <span>(ge2)</span> with positive leading coefficients, and let <span>({a_j (n)}_{nge1} quad (j=1,2,dots))</span> be sequences of algebraic integers in the field <span>(Q(q))</span> with suitable growth conditions. In this paper, we investigate linear independence over <span>(Q(q))</span> of the numbers</p><div><div><span>$$1,quad sum_{n=1}^{infty} frac{a_j (n)}{q^{f_j (n)}} quad (j=1,2,dots).$$</span></div></div><p> In particular, when <span>(a_j(n) quad (j=1,2,dots))</span> are polynomials of <i>n</i>, we give a linear independence criterion for the above numbers.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"341 - 364"},"PeriodicalIF":0.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230533","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":"Constructions on the Poincaré-disk","authors":"D. Veres","doi":"10.1007/s10474-025-01551-1","DOIUrl":"10.1007/s10474-025-01551-1","url":null,"abstract":"<div><p> This paper concerns with implementations of constructions in\u0000the Poincaré model of hyperbolic geometry and their applications to proofs of\u0000selected theorems. The main motivation is how some hyperbolic geometric \u0000statements can be proven using elementary methods within the model. By embedding\u0000hyperbolic geometry into the Euclidean plane, certain proofs can become more\u0000accessible and comprehensible.</p><p>In this paper, we present two elementary constructions developed by using\u0000the Poincaré model, followed by novel-approached answers to the following \u0000questions. Does a common perpendicular always exist for two ultraparallel lines? Can\u0000a given line segment be divided into <span>(n)</span> equal parts? Is it possible to construct a\u0000triangle from three given angles, provided their sum is less than 180 degrees?</p><p>Although there exist known answers to these questions, the usual proofs \u0000involve strong theorems or trigonometric functions requiring extensive calculations\u0000(e.g. [6] and [2]). Instead, hereby we present proofs using elementary tools with\u0000easily understandable steps.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"437 - 446"},"PeriodicalIF":0.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230539","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":"New weak Herz spaces with variable exponent and the boundedness of some sublinear operators","authors":"K. Matsuoka","doi":"10.1007/s10474-025-01542-2","DOIUrl":"10.1007/s10474-025-01542-2","url":null,"abstract":"<div><p>In the investigations of the boundedness of some sublinear operators, which do not hold the strong estimates, the researchers treat the weak estimates. In this occasion for the Herz spaces <span>(dot{K}_q^{alpha,p}({mathbb{R}}^n))</span>, in order to obtain more precise estimates \u0000than the weak estimates, the author [40] introduced the new “weak” Herz spaces <span>(widetilde{W}dot{K}_q^{alpha,p}({mathbb{R}}^n))</span> and showed the new “weak” boundedness on <span>(dot{K}_q^{alpha,p}({mathbb{R}}^n))</span>. In this paper, we will extend the above new “weak” estimates to the sublinear operators satisfying another size condition. Further, we will extend these results on the Herz spaces with constant exponents <span>(dot{K }_q^{alpha,p}({mathbb{R}}^n))</span> to one’s on the Herz spaces with variable exponent <span>(dot{K}_{q(cdot)}^{alpha,p}({mathbb{R}}^n))</span>. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"86 - 110"},"PeriodicalIF":0.6,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165612","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}