Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups

1999 ◽  
Vol 6 (1) ◽  
pp. 65-82
Author(s):  
V. Kokilashvili ◽  
A. Meskhi
Keyword(s):  
Singular Integrals ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Hardy Operator ◽  
Weighted Inequalities ◽  
Homogeneous Groups ◽  
Necessary And Sufficient

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.

scholarly journals On bilinear weighted inequalities with Volterra integral operators

2019 ◽  
Vol 486 (4) ◽  
pp. 416-420
Author(s):  
V. D. Stepanov ◽  
G. E. Shambilova
Keyword(s):  
Sufficient Conditions ◽  
Integral Operators ◽  
Necessary And Sufficient Conditions ◽  
Weighted Inequalities ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Necessary And Sufficient

Necessary and sufficient conditions on the boundedness in weighted Lebesgue spaces on the semiaxis for bilinear inequalities with Volterra integral operators are given.

scholarly journals Norm inequalities in multidimensional Lorentz spaces

2008 ◽  
Vol 103 (2) ◽  
pp. 278
Author(s):  
Boris Simonov ◽  
Sergey Tikhonov
Keyword(s):  
Trigonometric Series ◽  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Double Trigonometric Series ◽  
Norm Inequalities ◽  
Necessary And Sufficient

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

scholarly journals Two-Weighted Lp -Inequalities for Singular Integral Operators on Heisenberg Groups

1994 ◽  
Vol 1 (4) ◽  
pp. 367-376
Author(s):  
V. S. Guliev
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weight Functions ◽  
Weighted Inequalities ◽  
Heisenberg Groups

Abstract Some sufficient conditions are found for a pair of weight functions, providing the validity of two-weighted inequalities for singular integrals defined on Heisenberg groups.

Imbeddings Between Weighted Orlicz–Lorentz Spaces

1997 ◽  
Vol 4 (2) ◽  
pp. 117-128
Author(s):  
M. Krbec ◽  
J. Lang
Keyword(s):  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Abstract We establish necessary and sufficient conditions for imbeddings of weighted Orlicz–Lorentz spaces.

scholarly journals CRITERIA FOR THE BOUNDEDNESS AND COMPACTNESS OF INTEGRAL TRANSFORMS WITH POSITIVE KERNELS

2001 ◽  
Vol 44 (2) ◽  
pp. 267-284 ◽  
Author(s):  
A. Meskhi
Keyword(s):  
Borel Measure ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Integral Transforms ◽  
Necessary And Sufficient Conditions ◽  
Subject Classification ◽  
Necessary And Sufficient ◽  
Positive Kernels ◽  
Primary 46B50

AbstractThe necessary and sufficient conditions that guarantee the boundedness and compactness of integral operators with positive kernels from $L^p(a,b)$ to $L^q_{\nu}(a,b)$, where $p,q\in(1,\infty)$ or $0lt q\leq1lt plt\infty$, for a non-negative Borel measure $\nu$ on $(a,b)$ are found.AMS 2000 Mathematics subject classification: Primary 46B50; 47B34; 47B38

Riesz potential in the local Morrey–Lorentz spaces and some applications

2020 ◽  
Vol 27 (4) ◽  
pp. 557-567
Author(s):  
Vagif S. Guliyev ◽  
Abdulhamit Kucukaslan ◽  
Canay Aykol ◽  
Ayhan Serbetci
Keyword(s):  
Maximal Operator ◽  
Riesz Potential ◽  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Analytic Semigroups ◽  
Fractional Powers ◽  
Marcinkiewicz Operator ◽  
Fractional Maximal Operator ◽  
Necessary And Sufficient

AbstractIn this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential {I_{\alpha}} in the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}. This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}.

scholarly journals Generalized Hilbert integral operators on the Herz spaces

2009 ◽  
Vol 40 (2) ◽  
pp. 193-200
Author(s):  
Kuang Jichang
Keyword(s):  
Sufficient Conditions ◽  
Integral Operators ◽  
Necessary And Sufficient Conditions ◽  
Operator Norm ◽  
Herz Spaces ◽  
Norm Inequalities ◽  
Necessary And Sufficient ◽  
Hilbert Integral

This paper gives some necessary and sufficient conditions for the generalized Hilbert integral operators to be bounded on the Herz spaces. The corresponding new operator norm inequalities are obtained.

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