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.

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.

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.

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.

Uniform Convergence of Trigonometric Series with General Monotone Coefficients

2019 ◽  
Vol 71 (6) ◽  
pp. 1445-1463
Author(s):  
Mikhail Dyachenko ◽  
Askhat Mukanov ◽  
Sergey Tikhonov
Keyword(s):  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Trigonometric Series ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Monotone Coefficients ◽  
Fourier Sums ◽  
Necessary And Sufficient

AbstractWe study criteria for the uniform convergence of trigonometric series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such series.

scholarly journals Weighted norm inequalities and indices

2006 ◽  
Vol 4 (1) ◽  
pp. 43-71 ◽  
Author(s):  
Joaquim Martín ◽  
Mario Milman
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Rearrangement Invariant Spaces ◽  
Hardy Type ◽  
Necessary And Sufficient ◽  
Invariant Spaces ◽  
Hardy Type Operators

We extend and simplify several classical results on weighted norm inequalities for classical operators acting on rearrangement invariant spaces using the theory of indices. As an application we obtain necessary and sufficient conditions for generalized Hardy type operators to be bounded on?p(w),?p,8(w),Gp(w)andGp,8(w).

Sign in / Sign up

Export Citation Format

Share Document