Work

Martingale Hardy Orlicz–Lorentz–Karamata spaces and applications in Fourier analysis

Year: 2024

Type: article

Abstract: We summarize some results as well as we prove some new results about the Orlicz–Lorentz–Karamata spaces and martingale Hardy Orlicz–Lorentz–Karamata spaces. More precisely, Doob's maximal inequality for submartingales and Burkholder–Davis–Gundy inequality are presented. We also show some fundamental martingale inequalities and modular inequalities. Additionally, based on atomic decompositions, duality theorems and fractional integral operators are discussed. As applications in Fourier analysis, we consider the Walsh–Fourier series on Orlicz–Lorentz–Karamata spaces. The dyadic maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces are presented. The boundedness of maximal Fejér operator is proved, which further implies some convergence results of the Fejér means.

Source: Analysis Mathematica

DOI: 10.1007/s10476-024-00057-2

Authors: Z. Hao, F. Weisz

Institutions: Hunan University of Science and Technology, Eötvös Loránd University

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Natural Science Foundation of China, Eötvös Loránd Tudományegyetem, Scientific Research Foundation of Hunan Provincial Education Department