Weighted adams type theorem for the riesz fractional integral in generalized morrey space

Burtseva, Evgeniya; Samko, Natasha

doi:10.1515/fca-2016-0052

Cited by 9 publications

(8 citation statements)

References 23 publications

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“…The interest in studying generalized Morrey spaces comes not only from theoretical reasons, but also from their important role in getting optimal Sobolev type embeddings for critical exponents (see, for instance, [3] and [24]). …”

Section: Preliminariesmentioning

confidence: 99%

Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces

Almeida

2017

Nonlinear Analysis

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Abstract. We prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces). In particular, we obtain embeddings into a new Stummel class of functions with some vanishing property at innity. We also partially improve a known result on the coincidence of Stummel spaces with a modication of Morrey spaces where the supremum norm is replaced by an integral L p -norm.

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Section: Preliminariesmentioning

confidence: 99%

Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces

Almeida

2017

Nonlinear Analysis

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“…The proof is straightforward: use dyadic decomposition, which is the standard tool when working with Morrey type norm (see, for instance, [6,31]) for the interval I and apply Hölder inequality. We have…”

Section: On the Bergmanmentioning

confidence: 99%

“…We refer, for instance, to Lemma 3.2 from [6] for the estimation of the infinite sum via integral. 2…”

Section: On the Bergmanmentioning

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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“…Some weighted estimates for multi‐dimensional Hardy‐type operators were derived in generalized Morrey spaces in . Moreover, the weighted boundedness of some multi‐dimensional Hardy‐type operators from generalized Morrey to Orlicz–Morrey spaces was investigated in . For more information concerning Hardy‐type inequalities in Morrey type spaces and their applications we refer to , see also references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the weighted boundedness of some multi‐dimensional Hardy‐type operators from generalized Morrey to Orlicz–Morrey spaces was investigated in . For more information concerning Hardy‐type inequalities in Morrey type spaces and their applications we refer to , see also references therein. The above mentioned spaces are Banach function spaces of measurable functions with prescribed integrability properties.…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces

Burtseva

Persson

Samko

2018

Mathematische Nachrichten

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We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point x=0 to functions differentiable for x≠0 and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified Rn).

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Weighted adams type theorem for the riesz fractional integral in generalized morrey space

Abstract: We prove the boundedness of the Riesz fractional integration operator from a generalized Morrey space

Cited by 9 publications

References 23 publications

Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces

Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces

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

Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces

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