2010
DOI: 10.1007/s12215-010-0015-1
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Boundedness of commutators on Herz spaces with variable exponent

Abstract: Our aim in the present paper is to prove the boundedness of vectorvalued commutators on Herz spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.

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Cited by 95 publications
(42 citation statements)
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“…We will generalize this result to the case of variable exponent and also consider the boundedness on Herz spaces with variable exponent. Our main tools are some properties of variable exponent and BMO norms obtained by the author [11].…”
mentioning
confidence: 99%
“…We will generalize this result to the case of variable exponent and also consider the boundedness on Herz spaces with variable exponent. Our main tools are some properties of variable exponent and BMO norms obtained by the author [11].…”
mentioning
confidence: 99%
“…Recently, Izuki [19] established a relationship between Lebesgue space with variable exponent and space which can be stated in the form of the following lemma.…”
Section: Proofs Of the Main Resultsmentioning
confidence: 99%
“…Lemma 6 (see [23,24]). Suppose (⋅) ∈ B(R ), and then there exists a positive constant such that for each…”
Section: Boundedness Of Singular Integrals and Their Commutatorsmentioning
confidence: 99%