Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

Wang, Hua

doi:10.1186/s13660-016-1279-6

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…Remark 2.7. It is worth pointing out that in the classical case when V ≡ 0, Theorems 2.3, 2.4 and 2.5 have been proved by Komori and Shirai in [11], while Theorem 2.6 has been shown by the author in [20].…”

Section: Our Main Resultsmentioning

confidence: 95%

Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals

Wang

2020

Journal of Function Spaces

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Let L = −∆ + V be a Schrödinger operator on R d , d ≥ 3, where ∆ is the Laplacian operator on R d and the nonnegative potential V belongs to the reverse Hölder class RH s for s ≥ d/2. For given 0 < α < d, the fractional integrals associated to the Schrödinger operator L is defined byIn this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RH s for s ≥ d/2. Then we will establish the boundedness properties of the fractional integrals I α on these new spaces. Furthermore, weighted strong-type estimate for the corresponding commutator [b, I α ] in the framework of Morrey spaces is also obtained. The classes of weights, the classes of symbol functions as well as weighted Morrey spaces discussed in this paper are larger than A p,q , BMO(R d ) and L p,κ (µ, ν) corresponding to the classical case (that is V ≡ 0).

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Section: Our Main Resultsmentioning

confidence: 95%

Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals

Wang

2020

Journal of Function Spaces

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“…In order to deal with the end-point case of the commutators, we have to consider the following L log L-type space, which was introduced by the second author in [25,26] (for the unweighted case, see also [12] and [21]). Definition 1.7.…”

Section: Definition 16 ([10]mentioning

confidence: 99%

Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces

Wang

2017

Front. Math. China

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In this paper, we consider the boundedness properties of multilinear θ-type Calderón-Zygmund operators T θ recently introduced in the literature. First, we prove strong type and weak type estimates for multilinear θ-type Calderón-Zygmund operators on products of weighted Morrey spaces with multiple weights. Then we discuss strong type estimates for both multilinear commutators and iterated commutators of T θ on products of these spaces with multiple weights. Furthermore, the weak endpoint estimates for commutators of T θ and pointwise multiplication with functions in bounded mean oscillation are established too. MSC(2020): 42B20; 42B25; 47B38; 47G10

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Some estimates for the commutators of multilinear maximal function on Morrey-type space

Zhang

2021

Open Mathematics

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Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

Cited by 5 publications

References 31 publications

Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals

Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals

Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces

Some estimates for the commutators of multilinear maximal function on Morrey-type space

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