Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent

Izuki, Mitsuo; Nakai, Eiichi; Sawano, Yoshihiro

doi:10.5186/aasfm.2015.4032

Cited by 25 publications

(11 citation statements)

References 28 publications

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“…It says that, under the assumptions of Theorem 1.1, the space X(R) has an unconditional wavelet basis. Similar questions were considered earlier in [NPR14] and [INS15] under hypotheses on the space X(R), which are different from ours (see also [Ho11a,Ho11b,So97,W12]).…”

Section: Theorem 11 Implies That the Quotient Banach Algebrasupporting

confidence: 70%

Algebra of convolution type operators with continuous data on Banach function spaces

Fernandes

Karlovich

2019

Banach Center Publ.

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We show that if the Hardy-Littlewood maximal operator is bounded on a reflexive Banach function space X(R) and on its associate space X ′ (R), then the space X(R) has an unconditional wavelet basis. As a consequence of the existence of a Schauder basis in X(R), we prove that the ideal of compact operators K(X(R)) on the space X(R) is contained in the Banach algebra generated by all operators of multiplication aI by functions a ∈ C(Ṙ), wherė R = R ∪ {∞}, and by all Fourier convolution operators W 0 (b) with symbols b ∈ CX(Ṙ), the Fourier multiplier analogue of C(Ṙ).2010 Mathematics Subject Classification: Primary 47G10; Secondary 46E30, 42C40. Key words and phrases: Banach function space, wavelet basis, multiplication operator, Fourier convolution operator, compact operator, Hardy-Littlewood maximal operator. The paper is in final form and no version of it will be published elsewhere.[1]

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Section: Theorem 11 Implies That the Quotient Banach Algebrasupporting

confidence: 70%

Algebra of convolution type operators with continuous data on Banach function spaces

Fernandes

Karlovich

2019

Banach Center Publ.

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“…If p(·) ∈ LH(R n ) and w ∈ A p(·) , then T is bounded on L p(·) w . Notice that a closely related result was very recently proved in [11].…”

mentioning

confidence: 73%

On a dual property of the maximal operator on weighted variable 𝐿^{𝑝} spaces

Lerner¹

2017

Functional Analysis, Harmonic Analysis, And Image Processing

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“…The Muckenhoupt A p class with constant exponent p ∈ (1, ∞) firstly proposed by Muckenhoupt in [21]. The variable Muckenhoupt A p(•) was considered in [20,[22][23][24][25].…”

Section: Definitionmentioning

confidence: 99%

Weighted norm inequality for bilinear Calderón–Zygmund operators on Herz–Morrey spaces with variable exponents

Sheng-rong

2019

J Inequal Appl

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Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent

Cited by 25 publications

References 28 publications

Algebra of convolution type operators with continuous data on Banach function spaces

Algebra of convolution type operators with continuous data on Banach function spaces

On a dual property of the maximal operator on weighted variable 𝐿^{𝑝} spaces

Weighted norm inequality for bilinear Calderón–Zygmund operators on Herz–Morrey spaces with variable exponents

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