On Multipliers from Weighted Sobolev Spaces to Lebesgue Spaces

2017 ◽  
pp. 52-57
Author(s):  
Leili Kussainova ◽  
Aigul Myrzagaliyeva
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Lebesgue Spaces

scholarly journals Convolution Algebraic Structures Defined by Hardy-Type Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Pedro J. Miana ◽  
Juan J. Royo ◽  
Luis Sánchez-Lajusticia
Keyword(s):  
Sobolev Spaces ◽  
Banach Algebras ◽  
Weighted Sobolev Spaces ◽  
Integral Kernel ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Weighted Lebesgue Spaces ◽  
Banach Modules ◽  
Hardy Type Operator ◽  
Fractional Derivation

The main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products onℝ+). To do this, we consider some suitable kernels such that the Hardy-type operator is bounded in weighted Lebesgue spacesLωpℝ+forp≥1. We also show new inequalities in these weighted Lebesgue spaces. These results are applied to several concrete function spaces, for example, weighted Sobolev spaces and fractional Sobolev spaces defined by Weyl fractional derivation.

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

scholarly journals L q -differentials for weighted Sobolev spaces.

2000 ◽  
Vol 47 (1) ◽  
pp. 151-161 ◽  
Author(s):  
Jana Bj�rn
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces

Compact embeddings of some weighted Sobolev spaces on ℝN

1995 ◽  
Vol 117 (2) ◽  
pp. 333-338 ◽  
Author(s):  
Raffaele Chiappinelli
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Compact Embeddings ◽  
Measurable Functions ◽  
Image Position

Let ρ,ρ0,ρ1 be positive, measurable functions on ℝN. For 1 ≤ t < ∞, consider the weighted Lebesgue and Sobolev spaces

Some uniqueness results for singular elliptic problems

2015 ◽  
Vol 26 (03) ◽  
pp. 1550026 ◽  
Author(s):  
L. Caso ◽  
R. D'Ambrosio
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Open Subset ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Divergence Form ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Singular Data

We prove some uniqueness results for Dirichlet problems for second-order linear elliptic partial differential equations in non-divergence form with singular data in suitable weighted Sobolev spaces, on an open subset Ω of ℝn, n ≥ 2, not necessarily bounded or regular.

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