Sharp Maximal Inequalities and Its Application to Some Bilinear Estimates

Tsutsui, Yohei

doi:10.1007/s00041-010-9129-2

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Orlicz-campanato Spaces and Relations To Orlicz-morrey Spaces1

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2023

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Cited by 9 publications

(1 citation statement)

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“…To prove Lemma 6.7 we use the following local version good λ inequality: Lemma 6.8 (Tsutsui [42], Komori-Furuya [15]).…”

Section: Orlicz-campanato Spaces and Relations To Orlicz-morrey Spacesmentioning

confidence: 99%

Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

Shi

Arai

Nakai

2020

Preprint

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We consider the commutators [b, T ] and [b, I ρ ] on Orlicz-Morrey spaces, where T is a Calderón-Zygmund operator, I ρ is a generalized fractional integral operator and b is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional maximal operators on Orlicz-Morrey spaces. Moreover, we introduce Orlicz-Campanato spaces and establish their relations to Orlicz-Morrey spaces.

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“…To prove Lemma 6.7 we use the following local version good λ inequality: Lemma 6.8 (Tsutsui [42], Komori-Furuya [15]).…”

Section: Orlicz-campanato Spaces and Relations To Orlicz-morrey Spacesmentioning

confidence: 99%

Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

Shi

Arai

Nakai

2020

Preprint

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Weak‐type Fefferman–Stein inequality and commutators on weak Orlicz–Morrey spaces

Kawasumi

2023

Mathematische Nachrichten

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We consider the Fefferman–Stein inequality for weak Orlicz–Morrey spaces and the commutators and on weak Orlicz–Morrey spaces, where T is a Calderón–Zygmund operator, is a generalized fractional integral operator and b is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness from of and from a weak Orlicz Morrey space to another weak Orlicz–Morrey space. We use the Fefferman–Stein inequality to prove the boundedness of the commutators. Since weak Orlicz–Morrey spaces contain the weak Lebesgue, weak Orlicz and weak Morrey spaces as special cases, our results contain the bounedness on these function spaces which are also new results.

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Decomposition of Function Spaces and Its Applications

Sawano

2018

Theory of Besov Spaces

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Sharp Maximal Inequalities and Its Application to Some Bilinear Estimates

Cited by 9 publications

References 28 publications

Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

Commutators of integral operators with functions in Campanato spaces on Orlicz-Morrey spaces

Weak‐type Fefferman–Stein inequality and commutators on weak Orlicz–Morrey spaces

Decomposition of Function Spaces and Its Applications

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