Commutators of fractional maximal operator on generalized Orlicz–Morrey spaces

Deringoz, Fatih; Guliyev, Vagif S.; Hasanov, Sabir G.

doi:10.1007/s11117-017-0504-y

Cited by 18 publications

(7 citation statements)

References 26 publications

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“…Similar to (1.1), we can define two different kinds of commutator of the fractional maximal function as follows. The mapping property of [b, M α ] has been extensively studied; see [1,2,8,12,13,16,23,[25][26][27][28][29][30][31], for instance. There are some applications of nonlinear commutators in analysis.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Zhang

2019

J Inequal Appl

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Let 0 < α < n and M α be the fractional maximal function. The nonlinear commutator of M α and a locally integrable function b is given by [b, M α ](f) = bM α (f)-M α (bf). In this paper, we mainly give some necessary and sufficient conditions for the boundedness of [b, M α ] on variable Lebesgue spaces when b belongs to Lipschitz or BMO(R n) spaces, by which some new characterizations for certain subclasses of Lipschitz and BMO(R n) spaces are obtained.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Zhang

2019

J Inequal Appl

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show abstract

“…The mapping property of [b, M α ] has been extensively studied. See [1,2,8,12,13,16,23,25,26,27,28,29,30,31] for instance. There are some applications of nonlinear commutators in Analysis.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Zhang,

Si,

2019

Preprint

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Let 0 < α < n and M α be the fractional maximal function. The nonlinear commutator of M α and a locally integrable function b is given by [b, M α ](f ) = bM α (f )− M α (bf ). In this paper, we mainly give some necessary and sufficient conditions for the boundedness of [b, M α ] on variable Lebesgue spaces when b belongs to Lipschitz or BM O(R n ) spaces, by which some new characterizations for certain subclasses of Lipschitz and BM O(R n ) spaces are obtained.

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“…It was shown in [4] that the operator [b, M C ] can be used in studying the product of a function in H 1 (R n ) and a function in BMO(R n ). Later on, the L p → L q bounds for the commutators of fractional maximal operator have been studied by many authors (see [9,12,32]). The maximal commutator was first studied by García-Cuerva, Harboure, Segovia and Torrea [10] who showed that the maximal commutator of M C with b is bounded on L p (R n ) for 1 < p < ∞ if and only if b ∈ BMO(R n ).…”

Section: The Global Casementioning

confidence: 99%