Integral operators on B σ -Morrey-Campanato spaces

Abstract. The theory of generalized Besov-Morrey spaces and generalized Triebel-LizorkinMorrey spaces is developed. Generalized Morrey spaces, which T. Mizuhara and E. Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.

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“…Such attempts are made for B σ -function spaces, variable Lebesgue spaces and Orlicz spaces. See [24], [35,42] and [43], respectively.…”

Section: 7mentioning

confidence: 99%

Generalized Morrey spaces and trace operator

2015

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“…However, it is unknown that

M_{k}^{c}

and

M_{k}^{u c}

are bounded from

L^{1} false(ℓ^{u} false) false(X, μ false)

w L^{1} false(ℓ^{u} false) false(X, μ false)

in general. On the Euclidean space

R^{d}

with the usual metric and the Lebesgue measure, the boundedness are known by , see also [, p. 498], and extended to the classical Morrey spaces by . On spaces of homogeneous type the boundedness are known by .…”

Section: Resultsmentioning

confidence: 99%

Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

Sihwaningrum

Gunawan

Nakai

2018

Mathematische Nachrichten

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We establish the boundedness and weak boundedness of the maximal operator and generalized fractional integral operators on generalized Morrey spaces over metric measure spaces (X,d,μ) without the assumption of the growth condition on μ. The results are generalization and improvement of some known results. We also give the vector‐valued boundedness. Moreover we prove the independence of the choice of the parameter in the definition of generalized Morrey spaces by using the geometrically doubling condition in the sense of Hytönen.

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“…It is known that some classical operators are bounded on B σ (E)(R n ) andḂ σ (E)(R n ), see [25]. Applying the interpolation property, we extend these boundedness to B u w (E)(R n ) andḂ u w (E)(R n ).…”

Section: Boundedness Of Linear and Sublinear Operatorsmentioning

confidence: 89%

“…as R, S → ∞ for a.e. R n , or in L q loc (R n ), see [25,Lemmas 3 and 4]. Then, letting T f = lim R→∞ T (f χ R ) for f ∈ L p,λ (R n ), we can define T as a bounded operator from L p,λ (R n ) to L q,µ (R n ) or to W L q,µ (R n ), see [25,Remark 15] in which we point out that we need the condition (5.1).…”

Section: Singular and Fractional Integral Operatorsmentioning

confidence: 99%

$B_w^u$-function Spaces and Their Interpolation

Nakai

Sobukawa

2016

Tokyo J. Math.

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We introduce B u w -function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, B p , CMO, local Morrey-type spaces, etc., and investigate the interpolation property of B u w -function spaces. We also apply it to the boundedness of linear and sublinear operators, for example, the Hardy-Littlewood maximal and fractional maximal operators, singular and fractional integral operators with rough kernel, the Littlewood-Paley operator, Marcinkiewicz operator, and so on.

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Integral operators on B σ -Morrey-Campanato spaces

Cited by 27 publications

References 22 publications

Generalized Morrey spaces and trace operator

Generalized Morrey spaces and trace operator

Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

$B_w^u$-function Spaces and Their Interpolation

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