Variable Lebesgue Spaces

Cruz-Uribe, David; Fiorenza, Alberto

doi:10.1007/978-3-0348-0548-3

Cited by 684 publications

(210 citation statements)

References 8 publications

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“…For more information about L p(·) spaces, see [12], [17] and [29]. It is well known that (L p(·) (R n ), · p(·) ) is a Banach space.…”

Section: Introductionmentioning

confidence: 99%

Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

Bernardis¹,

Dalmasso²,

Pradolini³

2014

Ann. Acad. Sci. Fenn. Math.

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Abstract. We characterize the class of weights related to the boundedness of maximal operators associated to a Young function η in the context of variable Lebesgue spaces. Fractional versions of these results are also obtained by means of a weighted Hedberg type inequality. These results are new even in the classical Lebesgue spaces. We also deal with Wiener's type inequalities for the mentioned operators in the variable context. As applications of the strong type results for the maximal operators, we derive weighted boundedness properties for a large class of operators controlled by them.

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“…For more information about L p(·) spaces, see [12], [17] and [29]. It is well known that (L p(·) (R n ), · p(·) ) is a Banach space.…”

Section: Introductionmentioning

confidence: 99%

Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

Bernardis¹,

Dalmasso²,

Pradolini³

2014

Ann. Acad. Sci. Fenn. Math.

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“…Concerning references related to Log spaces (mostly for n = , or α = ), we refer the reader to the treatise [13] (see, in particular, Definition 2.2 in this reference), and to [14,16,18,[21][22][23].…”

Section: The Log Spaces D α (ω) An Intermediate Regularity Resultsmentioning

confidence: 99%

Moduli of continuity, functional spaces,\break and elliptic boundary value problems. The full regularity spaces C _α ^0,λ(Ω̅)

Veiga

2016

Advances in Nonlinear Analysis

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Let L be a second order uniformly elliptic operator, and consider the equation Lu = f under the boundary condition u = . We assume data f in generical subspaces of continuous functions D ω characterized by a given modulus of continuity ω(r), and show that the second order derivatives of the solution u belong to functional spaces Dω, characterized by a modulus of continuityω(r) expressed in terms of ω(r). Results are optimal. In some cases, as for Hölder spaces, Dω = D ω . In this case we say that full regularity occurs. In particular, full regularity occurs for the new class of functional spaces C ,λ α (Ω) which includes, as a particular case, the classical Hölder spaces C ,λ (Ω) = C ,λ (Ω). Few words, concerning the possibility of generalizations and applications to non-linear problems, are expended at the end of the introduction and also in the last section.

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“…As a matter of fact, major attention was paid to real variable settings. We refer to the books [7,8,25,26] (see also review paper [34]). …”

Section: Introductionmentioning

confidence: 99%

Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

Karapetyants

2017

FCAA

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The aim of the paper is twofold. First, we present a new general approach to the definition of a class of mixed norm spaces of analytic functions A q;X (D), 1 q < ∞ on the unit disc D. We study a problem of boundedness of Bergman projection in this general setting. Second, we apply this general approach for the new concrete cases when X is either Orlicz space or generalized Morrey space, or generalized complementary Morrey space. In general, such introduced spaces are the spaces of functions which are in a sense the generalized Hadamard type derivatives of analytic functions having l q summable Taylor coefficients.MSC 2010 : Primary 30H20; Secondary 46E30, 46E15

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Variable Lebesgue Spaces

Cited by 684 publications

References 8 publications

Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

Moduli of continuity, functional spaces,\break and elliptic boundary value problems. The full regularity spaces C _α ^0,λ(Ω̅)

Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

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Variable Lebesgue Spaces

Cited by 684 publications

References 8 publications

Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

Moduli of continuity, functional spaces,\break and elliptic boundary value problems. The full regularity spaces C α 0,λ(Ω̅)

Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces

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Moduli of continuity, functional spaces,\break and elliptic boundary value problems. The full regularity spaces C _α ^0,λ(Ω̅)