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Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups
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V. Kokilashvili
Published/Copyright:
February 24, 2010
Abstract
The optimal sufficient conditions are found for weights, which guarantee the validity of two-weighted inequalities for singular integrals in the Lorentz spaces defined on homogeneous groups. In some particular case the found conditions are necessary for the corresponding inequalities to be valid. Also, the necessary and sufficient conditions are found for pairs of weights, which provide the validity of two-weighted inequalities for the generalized Hardy operator in the Lorentz spaces defined on homogeneous groups.
Key words and phrases.: Hilbert transform; singular integrals; Hardy operator; Lorentz spaces; two-weighted inequality; homogeneous groups
Received: 1996-11-21
Published Online: 2010-02-24
Published in Print: 1999-February
© 1999 Plenum Publishing Corporation
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Keywords for this article
Hilbert transform;
singular integrals;
Hardy operator;
Lorentz spaces;
two-weighted inequality;
homogeneous groups
Articles in the same Issue
- Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures
- A Radial Derivative with Boundary Values of the Spherical Poisson Integral
- Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions
- On Periodic Solutions of Nonlinear Functional Differential Equations
- Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups
- On the Absolute Summability of Series with Respect to Block-Orthonormal Systems
- Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization
