scholarly journals Sobolev type spaces based on Lorentz-Karamata spaces

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3023-3032
Author(s):  
İlker Eryilmaz
Keyword(s):  
Banach Spaces ◽  
Sobolev Spaces ◽  
Sobolev Type ◽  
Measure Algebra ◽  
Multiplier Algebra ◽  
Integer Order ◽  
Convolution Algebras ◽  
Weak Factorization ◽  
Sobolev Type Spaces ◽  
Type Spaces

In this paper, firstly Lorentz-Karamata-Sobolev spaces Wk,(p,q,b) (Rn) of integer order are introduced and some of their important properties are emphasized. Also, Banach spaces Ak,L(p,q,b)(Rn) = L1(Rn)? Wk,L(p,q,b)(Rn) (Lorentz-Karamata-Sobolev algebras) are studied. Using a result of H.C.Wang, it is showed that Banach convolution algebras AkL(p,q,b)(Rn) don?t have weak factorization and the multiplier algebra of Ak,L(p,q,b)(Rn) coincides with the measure algebra M(Rn) for 1 < p < 1 and 1 ? q < 1.

scholarly journals Higher Order Sobolev-Type Spaces on the Real Line

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Bogdan Bojarski ◽  
Juha Kinnunen ◽  
Thomas Zürcher
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Finite Differences ◽  
Higher Order ◽  
Sobolev Type ◽  
The Real ◽  
Sobolev Functions ◽  
Sobolev Type Spaces ◽  
Type Spaces

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.

scholarly journals Approximate solutions of equations defined by complex spherical multiplier operators

2005 ◽  
Vol 2005 (2) ◽  
pp. 93-115
Author(s):  
C. P. Oliveira
Keyword(s):  
Approximate Solutions ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Sobolev Type ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Solutions Of Equations ◽  
Multiplier Operators

This paper studies, in a partial but concise manner, approximate solutions of equations defined by complex spherical multiplier operators. The approximations are from native spaces embedded in Sobolev-type spaces and derived from the use of positive definite functions to perform spherical interpolation.

Sharp Singular Trudinger–Moser Inequalities Under Different Norms

2019 ◽  
Vol 19 (2) ◽  
pp. 239-261 ◽  
Author(s):  
Nguyen Lam ◽  
Guozhen Lu ◽  
Lu Zhang
Keyword(s):  
Exponential Type ◽  
Sobolev Type ◽  
Infinite Volume ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
The Relationship

AbstractThe main purpose of this paper is to prove several sharp singular Trudinger–Moser-type inequalities on domains in {\mathbb{R}^{N}} with infinite volume on the Sobolev-type spaces {D^{N,q}(\mathbb{R}^{N})}, {q\geq 1}, the completion of {C_{0}^{\infty}(\mathbb{R}^{N})} under the norm {\|\nabla u\|_{N}+\|u\|_{q}}. The case {q=N} (i.e., {D^{N,q}(\mathbb{R}^{N})=W^{1,N}(\mathbb{R}^{N})}) has been well studied to date. Our goal is to investigate which type of Trudinger–Moser inequality holds under different norms when q changes. We will study these inequalities under two types of constraint: semi-norm type {\|\nabla u\|_{N}\leq 1} and full-norm type {\|\nabla u\|_{N}^{a}+\|u\|_{q}^{b}\leq 1}, {a>0}, {b>0}. We will show that the Trudinger–Moser-type inequalities hold if and only if {b\leq N}. Moreover, the relationship between these inequalities under these two types of constraints will also be investigated. Furthermore, we will also provide versions of exponential type inequalities with exact growth when {b>N}.

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