{"title":"Bergman-type and Qk-type spaces of p-harmonic functions","authors":"Xi Fu, X. Xie","doi":"10.54503/0002-3043-2022.57.3-73-88","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.3-73-88","url":null,"abstract":"In this paper, we extend a Hardy-Littlewood type theorem to the exponentially\u0000p-harmonic Bergman space on the real unit ball B in Rn. As an application, we characterize\u0000exponentially p-harmonic Bergman spaces in terms of Lipschitz type conditions. Furthermore, some derivative-free characterizations for n-harmonic Qk spaces are established.","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126805035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Мартин Геворгович Григорян, M. G. Grigoryan, Сергей Владимирович Конягин, S. Konyagin
{"title":"О рядах Фурье, почти универсальных в классе измеримых функций","authors":"Мартин Геворгович Григорян, M. G. Grigoryan, Сергей Владимирович Конягин, S. Konyagin","doi":"10.54503/0002-3043-2022.57.4-14-22","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.4-14-22","url":null,"abstract":"В работе построен такой универсальный тригонометрический ряд, что после умножения членов этого ряда на некоторую последовательность знаков {δk = ±1}∞ k=0 его можно превратить в ряд Фурье некоторой интегрируемой функции.","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130305284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some problems of convergence of general Fourier series","authors":"V. Tsagareishvili, G.Tutberidze","doi":"10.54503/0002-3043-2022.57.6-70-80","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.6-70-80","url":null,"abstract":"S. Banach [1] proved that good differential properties of function do not guarantee\u0000the a.e. convergence of the Fourier series of this function with respect to general orthonormal\u0000systems (ONS). On the other hand it is very well known that a sufficient condition for the a.e.\u0000convergence of an orthonormal series is given by the Menshov-Rademacher Theorem.\u0000The paper deals with sequence of positive numbers (dn) such that multiplying the Fourier\u0000coefficients (Cn(f)) of functions with bounded variation by these numbers one obtains a.e. convergent\u0000series of the form\u0000P∞\u0000n=1 dnCn(f)φn(x). It is established that the resulting conditions are best\u0000possible.","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123712136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Неравенства типа Марценкевича-Зигмундав вещественном шаре","authors":"К Р Аветисян","doi":"10.54503/0002-3043-2022.57.1-35-44","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.1-35-44","url":null,"abstract":"Установлены некоторые обобщения классического неравенства\u0000Марцинкевича–Зигмунда о мажорации g-функции Литтлвуда-Пэли для гармонических функций в единичном шаре пространства Rn.","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126706579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Центральные расширения n-крученых групп","authors":"Варужан Сергеевич Атабекян, Гегам Григорьевич Геворгян","doi":"10.54503/0002-3043-2022.57.1-19-34","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.1-19-34","url":null,"abstract":"В работе для n-крученых групп нечетного периода n ≥ 1003\u0000строится некоторая модификация метода, который был придуман С. И. Адяном для положительного решения известной проблемы о существовании некоммутативных аналогов аддитивной группы рациональных чисел с любым конечным числом порождающих, и с ее помощью доказывается, что любая\u0000m-порожденная абелева группа D может быть вложена в качестве центра в\u0000некоторую группу A так, что фактор группа A/D изоморфна заданной nкрученой группе с не менее чем m независимыми определяющими соотношениями. В качестве приложения доказывается, что каждая конечная подгруппа любой n-крученой группы является циклической, что обобщает аналогичный результат, доказанный ранее С. И .Адяном для свободных бернсайдовых\u0000групп нечетного периода n ≥ 665. Заметим, что множество неизоморфных\u0000s-порожденных n-крученых групп континуально для фиксированного s > 1\u0000и любого нечетного n ≥ 1003.","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114615472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Infinitely Many Solutions For Neuman Problems Associated To Non-Homogeneous Differential Operator Through Orlicz-Sobolev Spaces","authors":"A. Kashiri, G. Afrouzi","doi":"10.54503/0002-3043-2022.57.1-64-76","DOIUrl":"https://doi.org/10.54503/0002-3043-2022.57.1-64-76","url":null,"abstract":"The goal of this paper is to establish the existence of an unbounded sequence\u0000of weak solutions for the following non-homogeneous Neumann problem","PeriodicalId":388049,"journal":{"name":"Proceedings of NAS RA. Mathematics","volume":"184 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134395717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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