Compact Commutators of Calderón-Zygmund and Generalized Fractional Integral Operators with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces

Arai, Ryutaro; Nakai, Eiichi

doi:10.3836/tjm/1502179285

Cited by 14 publications

(11 citation statements)

References 33 publications

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“…Proof. We prove the theorem in the case (2). Under these assumptions and the conditions appearing in the conclusion of theorem, we check that we can find parameters σ and q + , q − as in the Lemma 7.3.…”

mentioning

confidence: 81%

“…The following result of Arai-Nakai [2], based on Sawano and Shirai's method [35], provides a concrete condition to verify the assumptions of Corollary 4.6: Theorem 5.2 ( [2]). Let 0 < λ < d, 1 < p < ∞ and T be a Calderón-Zygmund operator that extends to a bounded operator on L 2 (R d ).…”

Section: Suppose Moreover Thatmentioning

confidence: 99%

“…In[2], Theorem 5.2 is stated and proved in the setting of the generalized Morrey spaceL (p,φ) (R d ), where φ : R d × (0, ∞) → (0, ∞) is a variable growth function. This space coincides with L p,λ (R d ) by choosing φ(x, r) = |B(x, r)| λ/d−1, where B = B(x, r) is the ball with center x and radius r.By combining Corollary 4.6 and Theorems 5.1 and 5.2 we obtain the following result which appears to be new:Let 1 < p + < ∞, 1 < σ < ∞, p − = max {1, p + (1 − 1/σ)},and 0 < λ < d−d/σ.…”

mentioning

confidence: 99%

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Extrapolation of compactness on weighted Morrey spaces

Lappas

2022

Studia Math.

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In a previous work, "compact versions" of Rubio de Francia's weighted extrapolation theorem were proved, which allow one to extrapolate the compactness of a linear operator from just one space to the full range of weighted Lebesgue spaces where this operator is bounded. In this paper, we extend these results to the setting of weighted Morrey spaces. As applications, we easily obtain new results on the weighted compactness of commutators of Calderón-Zygmund singular integrals, rough singular integrals and Bochner-Riesz multipliers.

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mentioning

confidence: 81%

Section: Suppose Moreover Thatmentioning

confidence: 99%

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confidence: 99%

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Extrapolation of compactness on weighted Morrey spaces

Lappas

2022

Studia Math.

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“…The following result of Arai-Nakai [2], based on Sawano and Shirai's method in [36], provides a concrete condition to verify the assumptions of Corollary 4.6: Proof. Let us fix some σ 1 ∈ (1, ∞), λ 1 ∈ (0, d − d σ 1 ), p 1 ∈ [p − , p + ] and p1 ∈ (1, ∞) for which we verify the assumptions of Corollary 4.6 with κ = 1.…”

Section: Commutators Of Calderón-zygmund Singular Integralsmentioning

confidence: 99%

Extrapolation of compactness on weighted Morrey spaces

Lappas

2021

Preprint

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In two previous works, "compact versions" of Rubio de Francia's weighted extrapolation theorem were proved, which allow one to extrapolate the compactness of an linear operator from just one space to the full range of weighted Lebesgue spaces, where this operator is bounded. In this paper, we extend these results to the setting of weighted Morrey spaces. As applications, we easily obtain new results on the weighted compactness of commutators of Calderón-Zygmund singular integrals, rough singular integrals and Bochner-Riesz multipliers.

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“…In addition, note that if p − ∈ (1, ∞), then H p (•) A (R n ) = L p(•) (R n ) with equivalent quasi-norms (see [46,Corollary 4.20]). Thus, in this case, it follows from Cruz-Uribe and Fiorenza [7,Theorem 2.80] that the dual space of H p(•) A (R n ) is just the variable Lebesgue space L p(•) ′ (R n ), where conjugate exponent function p(•) ′ is defined by setting 1 p(•) + 1 p(•) ′ = 1. Obviously, there is a gap between two ranges 0 < p − ≤ p + ≤ 1 and p − ∈ (1, ∞).…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Variable Campanato-Type Spaces and Their Carleson Measure Characterizations

Huang¹

2021

Preprint

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Let p(•) : R n → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on R n . In this article, the authors introduce the anisotropic variable Campanato-type spaces and give some applications. Especially, using the known atom and finite atom characterizations of anisotropic variable Hardy space H p(•) A (R n ), the authors prove that this Campanato-type space is the appropriate dual space of H p(•) A (R n ) with full range p(•). As applications, the authors first deduce several equivalent characterizations of these Campanato-type spaces. Furthermore, the authors also introduce the anisotropic variable tent spaces and show their atomic decomposition. Combining this and the obtained dual theorem, the Carleson measure characterizations of these anisotropic variable Campanato-type spaces are established.

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Compact Commutators of Calderón-Zygmund and Generalized Fractional Integral Operators with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces

Cited by 14 publications

References 33 publications

Extrapolation of compactness on weighted Morrey spaces

Extrapolation of compactness on weighted Morrey spaces

Extrapolation of compactness on weighted Morrey spaces

Anisotropic Variable Campanato-Type Spaces and Their Carleson Measure Characterizations

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