Weighted estimates for fractional integral operators on central Morrey spaces

Komori-Furuya, Yasuo; Sato, Enji

doi:10.1002/mana.201700013

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Introduction and The Main Results1

Necessary Conditions For Fractional Operators1

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2020

2022

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Cited by 4 publications

(2 citation statements)

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“…Fractional type operators are a class of important operators in harmonic analysis and were widely used in the study of partial differential equations and function spaces [1, 2, 4–6, 9, 15, 20, 22, 30]. Recall that the fractional maximal function

M_{α}

and the fractional integral operator

I_{α}

are defined by

M_{α} f false(x false) : = \underset{Q ∋ x}{trueprefixsup} \frac{1}{{false| Q false|}^{1 - α / n}} \int_{Q} false| f false|, 0 < α < n,

and

I_{α} f false(x false) : = \int_{R^{n}} \frac{f (y)}{{false| x - y false|}^{n - α}}, 0 < α < n,

respectively, where f is a locally integrable function defined on

R^{n}

and Q takes over all cubes in

R^{n}

which contain x .…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Two‐weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

Pan

Sun

2020

Mathematische Nachrichten

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M_{α}

and the fractional integral operator

I_{α}

are defined by

M_{α} f false(x false) : = \underset{Q ∋ x}{trueprefixsup} \frac{1}{{false| Q false|}^{1 - α / n}} \int_{Q} false| f false|, 0 < α < n,

and

I_{α} f false(x false) : = \int_{R^{n}} \frac{f (y)}{{false| x - y false|}^{n - α}}, 0 < α < n,

respectively, where f is a locally integrable function defined on

R^{n}

and Q takes over all cubes in

R^{n}

which contain x .…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Two‐weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

Pan

Sun

2020

Mathematische Nachrichten

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“…For weighted inequalities in the Adams range on global Morrey spaces see [8] and [15]. Let us mention that it is possible to obtain an Adams-type result on (unweighted) local Morrey spaces if we restrict the action of the operator to radial functions (see [10] and [11]).…”

Section: Necessary Conditions For Fractional Operatorsmentioning

confidence: 99%

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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Singular and Fractional Integral Operators on Weighted Local Morrey Spaces

Duoandikoetxea¹,

Rosenthal²

2022

J Fourier Anal Appl

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Weighted estimates for fractional integral operators on central Morrey spaces

Cited by 4 publications

References 10 publications

Two‐weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

Two‐weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

Singular and fractional integral operators on weighted local Morrey spaces

Singular and Fractional Integral Operators on Weighted Local Morrey Spaces

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