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Extrapolation to product Herz spaces and some applications

Extrapolation to product Herz spaces and some applications AbstractThis paper extends the extrapolation theory to product Herz spaces. To prove the main result, we first investigate the dual space of the product Herz space, and then show the boundedness of the strong maximal operator on product Herz spaces. By using this extrapolationtheory, we establish the John–Nirenberg inequality, the characterization of little bmo, the Fefferman–Stein vector-valued inequality, the boundedness of the bi-parameter singular integral operator, the strong fractional maximal operator, and the bi-parameter fractional integral operator on product Herz spaces. We also give a new characterization of little bmo via the boundedness of the commutators of some bi-parameter operators on product Herz spaces.Even in the one-parameter setting, some of our results are new. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Extrapolation to product Herz spaces and some applications

Forum Mathematicum , Volume 33 (5): 27 – Sep 1, 2021

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References (49)

Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2021-0060
Publisher site
See Article on Publisher Site

Abstract

AbstractThis paper extends the extrapolation theory to product Herz spaces. To prove the main result, we first investigate the dual space of the product Herz space, and then show the boundedness of the strong maximal operator on product Herz spaces. By using this extrapolationtheory, we establish the John–Nirenberg inequality, the characterization of little bmo, the Fefferman–Stein vector-valued inequality, the boundedness of the bi-parameter singular integral operator, the strong fractional maximal operator, and the bi-parameter fractional integral operator on product Herz spaces. We also give a new characterization of little bmo via the boundedness of the commutators of some bi-parameter operators on product Herz spaces.Even in the one-parameter setting, some of our results are new.

Journal

Forum Mathematicumde Gruyter

Published: Sep 1, 2021

Keywords: Product Herz space; extrapolation; John–Nirenberg inequality; little bmo; commutator; 42B20; 42B25; 42B35

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