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).

scholarly journals A note on two-weight inequalities for multiple Hardy-type operators

2005 ◽  
Vol 3 (3) ◽  
pp. 223-237 ◽  
Author(s):  
Alexander Meskhi
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient ◽  
Hardy Type Operators

Necessary and sufficient conditions on a pair of weights guaranteeing two-weight estimates for the multiple Riemann-Liouville transforms are established provided that the weight on the right-hand side satisfies some additional conditions.

Hermite-Fejér interpolation with Jacobi weights

2011 ◽  
Vol 48 (3) ◽  
pp. 408-420
Author(s):  
G. Mastroianni ◽  
J. Szabados
Keyword(s):  
Error Estimates ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
Interpolation Process ◽  
Weighted Norm ◽  
Jacobi Weights ◽  
Jacobi Weight ◽  
Necessary And Sufficient

We consider the weighted Hermite-Fejér interpolation process based on Jacobi nodes for classes of locally continuous functions defined by another Jacobi weight. Necessary and sufficient conditions for the weighted norm boundedness and for the convergence, as well as error estimates of the approximation, are given.

Optimal rearrangement invariant range for Hardy-type operators

2016 ◽  
Vol 146 (4) ◽  
pp. 865-893 ◽  
Author(s):  
Javier Soria ◽  
Pedro Tradacete
Keyword(s):  
Monotone Operators ◽  
Hardy Operator ◽  
Optimal Range ◽  
Range Space ◽  
Optimal Domain ◽  
Rearrangement Invariant Spaces ◽  
Hardy Type ◽  
Invariant Spaces ◽  
Hardy Type Operators

We characterize, in the context of rearrangement invariant spaces, the optimal range space for a class of monotone operators related to the Hardy operator. The connection between the optimal range and the optimal domain for these operators is carefully analysed.

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.

Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions

2019 ◽  
Vol 150 (1) ◽  
pp. 17-39 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Júlio S. Neves
Keyword(s):  
Sufficient Conditions ◽  
Type Inequality ◽  
Weighted Norm ◽  
Hardy Type Inequality ◽  
Weighted Function ◽  
Hardy Type ◽  
Quasiconcave Functions ◽  
Measurable Functions ◽  
Image Position ◽  
Necessary And Sufficient

AbstractLet ρ be a monotone quasinorm defined on ${\rm {\frak M}}^ + $, the set of all non-negative measurable functions on [0, ∞). Let T be a monotone quasilinear operator on ${\rm {\frak M}}^ + $. We show that the following inequality restricted on the cone of λ-quasiconcave functions $$\rho (Tf) \les C_1\left( {\int_0^\infty {f^p} v} \right)^{1/p},$$where $1\les p\les \infty $ and v is a weighted function, is equivalent to slightly different inequalities considered for all non-negative measurable functions. The case 0 < p < 1 is also studied for quasinorms and operators with additional properties. These results in turn enable us to establish necessary and sufficient conditions on the weights (u, v, w) for which the three weighted Hardy-type inequality $$\left( {\int_0^\infty {{\left( {\int_0^x f u} \right)}^q} w(x){\rm d}x} \right)^{1/q} \les C_1\left( {\int_0^\infty {f^p} v} \right)^{1/p},$$holds for all λ-quasiconcave functions and all 0 < p, q ⩽ ∞.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

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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