A new approach to norm inequalities on weighted and variable Hardy spaces
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 $L^\infty$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.01519
- arXiv:
- arXiv:1902.01519
- Bibcode:
- 2019arXiv190201519C
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 42B20;
- 42B25;
- 42B30;
- 42B35
- E-Print:
- A couple minor typos corrected. Removed "showkeys" package for easier reading