Muckenhoupt-Type Conditions on Weighted Morrey Spaces

Duoandikoetxea, Javier; Rosenthal, Marcel

doi:10.1007/s00041-021-09839-w

Cited by 12 publications

(7 citation statements)

References 22 publications

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“…Nevertheless, a remarkable result of S. Nakamura, Y. Sawano, and H. Tanaka in [16] gives necessary and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator M on weighted local Morrey spaces. In [4] the authors of this paper obtained a simplified characterization of the same result in the form of a Muckenhoupt-type condition adapted to the Morrey setting. More precisely, we showed that the condition (1.2) sup…”

Section: Introductionmentioning

confidence: 94%

“…Let T be a Calderón-Zygmund operator associated to the kernel K and f ∈ LM p (ϕ, w) with w satisfying (1.3). Since (1.3) is stronger than (1.2), we know that w ∈ A p,loc (see [4,Lemma 6.2]). Let B be a ball such that…”

Section: Calderón-zygmund Operators On Weighted Local Morrey Spacesmentioning

confidence: 99%

“…Before characterizing the weights for M α we prove a lemma, similar to Lemma 6.2 in [4]. We use the notation ϕ p to denote the function such that ϕ p (B) = ϕ(B) p as mentioned in the introduction.…”

Section: Sufficient Conditions For Fractional Operatorsmentioning

confidence: 99%

“…We remark that due to the lack of density of smooth functions in the Morrey-type spaces the operators need to be defined in a convenient way. Condition (1.3) is the limiting case of the sufficient condition obtained in [4,Theorem 7.3] by using extrapolation of Lebesgue-weighted inequalities.…”

Section: Introductionmentioning

confidence: 99%

“…In our approach in [4] a crucial role was played by the local Hardy-Littlewood maximal operator, where local refers to the use of balls separated from the origin. These operators and their weighted inequalities were studied in [13] and [6].…”

Section: Introductionmentioning

confidence: 99%

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Singular and fractional integral operators on weighted local Morrey spaces

Duoandikoetxea¹,

Rosenthal²

2021

Preprint

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We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calderón-Zygmund operators suitably defined on the functions of the space. In the case of the fractional maximal operator and the fractional integral we obtain a characterization valid for exponents satisfying the Sobolev relation. For power weights we get sharp results in a larger range of exponents for the usual versions of weighted Morrey spaces.

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Section: Introductionmentioning

confidence: 94%

Section: Calderón-zygmund Operators On Weighted Local Morrey Spacesmentioning

confidence: 99%

Section: Sufficient Conditions For Fractional Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Singular and fractional integral operators on weighted local Morrey spaces

Duoandikoetxea¹,

Rosenthal²

2021

Preprint

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Weighted Boundedness of Certain Sublinear Operators in Generalized Morrey Spaces on Quasi-Metric Measure Spaces Under the Growth Condition

Samko

2022

J Fourier Anal Appl

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We prove weighted boundedness of Calderón–Zygmund and maximal singular operators in generalized Morrey spaces on quasi-metric measure spaces, in general non-homogeneous, only under the growth condition on the measure, for a certain class of weights. Weights and characteristic of the spaces are independent of each other. Weighted boundedness of the maximal operator is also proved in the case when lower and upper Ahlfors exponents coincide with each other. Our approach is based on two important steps. The first is a certain transference theorem, where without use homogeneity of the space, we provide a condition which insures that every sublinear operator with the size condition, bounded in Lebesgue space, is also bounded in generalized Morrey space. The second is a reduction theorem which reduces weighted boundedness of the considered sublinear operators to that of weighted Hardy operators and non-weighted boundedness of some special operators.

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Singular and Fractional Integral Operators on Weighted Local Morrey Spaces

Duoandikoetxea¹,

Rosenthal²

2022

J Fourier Anal Appl

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Muckenhoupt-Type Conditions on Weighted Morrey Spaces

Cited by 12 publications

References 22 publications

Singular and fractional integral operators on weighted local Morrey spaces

Singular and fractional integral operators on weighted local Morrey spaces

Weighted Boundedness of Certain Sublinear Operators in Generalized Morrey Spaces on Quasi-Metric Measure Spaces Under the Growth Condition

Singular and Fractional Integral Operators on Weighted Local Morrey Spaces

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