Musielak–Orlicz–Lorentz Hardy Spaces:Maximal Function,Finite Atomic,and Littlewood–Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms  

作　　者：Hongchao Jia Der-Chen Chang Ferenc Weisz Dachun Yang Wen Yuan 

机构地区：[1]Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China [2]Department of Mathematics and Statistics,Georgetown University,Washington,DC 20057,USA [3]Graduate Institute of Business Administration,College of Management,Fu Jen Catholic University,New Taipei City 242,Taiwan,China [4]Department of Numerical Analysis,Eotvos L.University,P´azm´any P.s´et´any 1/C.,Budapest 1117,Hungary

出　　处：《Acta Mathematica Sinica,English Series》2025年第1期1-77,共77页数学学报(英文版)

基　　金：partially supported by the National Key Research and Development Program of China(Grant No.2020YFA0712900);the National Natural Science Foundation of China(Grant Nos.12371093,12071197,and 12122102);the Fundamental Research Funds for the Central Universities(Grant No.2233300008);partially supported by a McDevitt Endowment Fund at Georgetown University。

摘　　要：Let q∈(0,∞]andϕbe a Musielak-Orlicz function with uniformly lower type p_(ϕ)^(−)∈(0,∞)and uniformly upper type p_(ϕ)^(−)∈(0,∞).In this article,the authors establish various realvariable characterizations of the Musielak-Orlicz-Lorentz Hardy space H^(ϕ,q)(R^(n)),respectively,in terms of various maximal functions,finite atoms,and various Little wood-Paley functions.As applications,the authors obtain the dual space of Hϕ,q(Rn)and the summability of Fourier transforms from Hϕ,q(Rn)to the Musielak-Orlicz-Lorentz space L^(ϕ,q)(R^(n))when q∈(0,∞)or from the Musielak-Orlicz Hardy space Hϕ(Rn)to Lϕ,∞(Rn)in the critical case.These results are new when q∈(0,∞)and also essentially improve the existing corresponding results(if any)in the case q=∞via removing the original assumption thatϕis concave.To overcome the essential obstacles caused by both thatϕmay not be concave and that the boundedness of the powered Hardy-Littlewood maximal operator on associated spaces of Musielak-Orlicz spaces is still unknown,the authors make full use of the obtained atomic characterization of H^(ϕ,q)(R^(n)),the corresponding results related to weighted Lebesgue spaces,and the subtle relation between Musielak-Orlicz spaces and weighted Lebesgue spaces.

关 键 词：Musielak-Orlicz-Lorentz Hardy space finite atom duality Littlewood-Paley characterization Fourier transform 

分 类 号：O177[理学—数学]