Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 175-198

A NEW APPROACH TO NORM INEQUALITIES ON WEIGHTED AND VARIABLE HARDY SPACES

David Cruz-Uribe, OFS, Kabe Moen and Hanh Van Nguyen

University of Alabama, Department of Mathematics
Tuscaloosa, AL 35487, U.S.A.; dcruzuribe 'at' ua.edu

University of Alabama, Department of Mathematics
Tuscaloosa, AL 35487, U.S.A.; kabe.moen 'at' ua.edu

University of Alabama, Department of Mathematics
Tuscaloosa, AL 35487, U.S.A.; hanhnguyenvan 'at' gmail.com

Abstract. We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of L^∞ atoms, vector-valued inequalities for maximal and other operators, and Rubio de Francia extrapolation. Many of these estimates are not new, but we give new and substantially simpler proofs, which in turn significantly simplifies the proofs of the Hardy spaces inequalities.

2010 Mathematics Subject Classification: Primary 42B20, 42B25, 42B30, 42B35.

Key words: Weighted Hardy spaces, variable Hardy spaces, extrapolation, singular integrals, fractional integrals.

Reference to this article: D. Cruz-Uribe, OFS, K. Moen and H. V. Nguyen: A new approach to norm inequalities on weighted and variable Hardy spaces. Ann. Acad. Sci. Fenn. Math. 45 (2020), 175-198.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4526