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 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 A generalization of the Paley–Wiener theorem for Mellin transforms and metric characterization of function spaces

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Paul L. Butzer ◽  
Ilaria Mantellini ◽  
Gerhard Schmeisser
Keyword(s):  
Asymptotic Behavior ◽  
Mellin Transform ◽  
Sobolev Type ◽  
Mellin Transforms ◽  
Metric Characterization ◽  
Wiener Theorem ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Prescribed Asymptotic Behavior

AbstractWe characterize the function space whose elements have a Mellin transform with exponential decay at infinity. This result can be seen as a generalization of the Paley–Wiener theorem for Mellin transforms. As a byproduct in a similar spirit, we also characterize spaces of functions whose distances from Mellin–Paley–Wiener spaces have a prescribed asymptotic behavior. This leads to Mellin–Sobolev type spaces of fractional order.

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.

A duality principle in weighted Sobolev spaces on the real line

2015 ◽  
Vol 288 (8-9) ◽  
pp. 877-897 ◽  
Author(s):  
Simon P. Eveson ◽  
Vladimir D. Stepanov ◽  
Elena P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
Duality Principle ◽  
The Real
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