Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces

Deringoz, Fatih; Guliyev, Vagif S.

doi:10.5186/aasfm.2015.4029

Cited by 19 publications

(14 citation statements)

References 22 publications

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“…For mapping properties in the so-called Musielak-Orlicz spaces we refer to [65]. In the case of Orlicz-Morrey spaces more general results were obtained in [9], including weak-type statements, and in [10] for vanishing Orlicz-Morrey spaces.…”

Section: Multidimensional Casementioning

confidence: 99%

Fractional Integrals and Derivatives: Mapping Properties

Rafeiro¹

2016

FCAA

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This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known, the fractional integrals defined in this or other forms improve in some sense the properties of the functions, at least locally, while fractional derivatives to the contrary worsen them. With the development of functional analysis this simple fact led to a number of important results on the mapping properties of fractional integrals in various function spaces.In the one-dimensional case we consider both Riemann-Liouville and Liouville forms of fractional integrals and derivatives. In the multidimensional case we consider in particular mixed Liouville fractional integrals, Riesz fractional integrals of elliptic and hyperbolic type and hypersingular integrals. Among the function spaces considered in this survey, the reader can find Hölder spaces, Lebesgue spaces, Morrey spaces, Grand spaces and also weighted and/or variable exponent versions.

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Section: Multidimensional Casementioning

confidence: 99%

Fractional Integrals and Derivatives: Mapping Properties

Rafeiro¹

2016

FCAA

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“…Recently, the studies of Morrey spaces is extending to Morrey space built on some non Lebesgue spaces such as Morrey-Lorentz spaces [3,18,31], Orlicz-Morrey spaces [11,29,28], Morrey spaces with variable exponents [1,13,15,19,22,24,25,26,33,32]. On the other hand, for instance, in [15,19], we are lack of a precise definition of the action of singular integral operators on the above mentioned Morrey type spaces.…”

Section: Introductionmentioning

confidence: 99%

Definability of singular integral operators on Morrey–Banach spaces

2020

J. Math. Soc. Japan

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We give a definition of singular integral operators on Morrey-Banach spaces which include Orlicz-Morrey spaces and Morrey spaces with variable exponents. The main result of this paper ensures that the singular integral operator is well defined on the Morrey-Banach spaces. Therefore, it provides a solid foundation for the study of singular integral operators on Morrey type spaces. As an application of our main result, we study the commutators of singular integral operators on Morrey-Banach spaces.

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“…Also Ragusa [44] proved a sufficient condition for commutators of fractional integral operators to belong to vanishing Morrey spaces V M p,λ (R n ) . The vanishing generalized Morrey spaces V M p,ϕ (R n ) were introduced and studied by Samko in [46], see also [3,17,37]. As it is known, last two decades there is an increasing interest to the study of variable exponent spaces and operators with variable parameters in such spaces, we refer for instance to the surveying papers [16,32,47], on the progress in this field, including topics of Harmonic Analysis and Operator Theory, see also references therein.…”

Section: Introductionmentioning

confidence: 99%

Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent

Guliyev¹,

Hasanov²,

Badalov³

2019

Mathematical Inequalities &Amp; Applications

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Let Ω ⊂ R n be an unbounded open set. We consider the generalized weighted Morrey spaces M p(·),ϕ ω (Ω) and the vanishing generalized weighted Morrey spaces V M p(·),ϕ ω (Ω) with variable exponent p(x) and a general function ϕ(x, r) defining the Morrey-type norm. The main result of this paper are the boundedness of Riesz potential and its commutators on the spaces M p(·),ϕ ω (Ω) and V M p(·),ϕ ω (Ω) . This result generalizes several existing results for Riesz potential and its commutators on Morrey type spaces. Especially, it gives a unified result for generalized Morrey spaces and variable Morrey spaces which currently gained a lot of attentions from researchers in theory of function spaces.

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Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces

Cited by 19 publications

References 22 publications

Fractional Integrals and Derivatives: Mapping Properties

Fractional Integrals and Derivatives: Mapping Properties

Definability of singular integral operators on Morrey–Banach spaces

Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent

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