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On the Predual of a Morrey–Lorentz Space and Its Applications to the Linear Calderón–Zygmund Operators
Our main purpose in this paper is to construct a predual of Morrey–Lorentz space via the block spaces, defined in [Ann. Scuola Norm. Sup. Pisa Cl....
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Boundedness and Compactness for the Commutator of the ω-Type Calderón-Zygmund Operator on Lorentz Space
In this paper, the authors consider the ω -type Calderón-Zygmund operator T ω and the commutator [ b, T ω ] generated by a symbol function b on the...
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Equivalent conditions of complete convergence and Marcinkiewicz–Zygmund-type strong law of large numbers for i.i.d. sequences under sub-linear expectations
Under suitable conditions, we study the equivalent conditions of complete convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers...
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The Schatten Classes of Calderón–Zygmund Operators
We prove sufficient conditions for a Calderón–Zygmund operator to belong to the Schatten classes. As in the classical T 1 theory, the conditions are...
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Exotic Calderón–Zygmund Operators
We study singular integral operators with kernels that are more singular than standard Calderón–Zygmund kernels, but less singular than bi-parameter...
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Calderón—Zygmund Operators and Commutators in Spaces of Homogeneous Type: Weighted Inequalities
The recent proof of the sharp weighted bound for Calderón-Zygmund operators has led to much investigation in sharp mixed bounds for operators and...
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Diversity of Lorentz-Zygmund Spaces of Operators Defined by Approximation Numbers
We prove the following dichotomy for the spaces ℒ
p , q , α ( a ) ( X , Y ) of all operators T ∈ ℒ ( X , Y ) whose approximation numbers belong to the... -
Approximate Characteristics of Generalized Poisson Operators on Zygmund Classes
The authors analyze approximate characteristics of generalized Poisson operators on Zygmund classes Z α , with the aim of their further application in...
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Riesz–Zygmund Means and Approximation in Variable Exponent Grand Spaces
In the paper, the estimates of generalized modulus of smoothness and best approximation in variable exponent grand Lebesgue spaces in terms of norms...
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Singular Integral Operators in Zygmund Spaces on Domains
Given a bounded Lipschitz domain D ⊂ ℝ d and a Calderón-Zygmund operator T , we study relations between smoothness properties of ∂ D and the boundedness...
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Strongly singular Calderón–Zygmund operators on Hardy spaces associated with ball quasi-Banach function spaces
We obtain the map** properties of the strongly singular Calderón–Zygmund operators on Hardy spaces associated with ball quasi-Banach function...
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Riesz–Zygmund means and trigonometric approximation in Morrey spaces
We estimate best approximations and moduli of smoothness of functions in Morrey spaces variable exponent spaces by norms of derivatives of...
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Calderón–Zygmund Type Results for a Class of Quasilinear Elliptic Equations Involving the p(x)-Laplacian
In this study, we obtain global Calderón–Zygmund-type estimates for weak solutions to quasilinear elliptic equations driven by p ( x )-Laplacian...
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The Riesz–Zygmund Sums of Fourier–Chebyshev Rational Integral Operators and Their Approximation Properties
Studying the approximation properties of a certain Riesz–Zygmund sum of Fourier–Chebyshev rational integral operators with constraints on the number...