From Arzelà–Ascoli to Riesz–Kolmogorov

作者: Przemysław Górka , Humberto Rafeiro

DOI: 10.1016/J.NA.2016.06.004

关键词:

摘要: Abstract In this paper we study totally bounded sets in Banach function spaces (BFS), from which characterize compact (via Hausdorff criterion) some non-standard fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for grand variable exponent Lebesgue spaces.

参考文章(28)
Marcel Riesz, Sur les ensembles compacts de fonctions sommables Springer Collected Works in Mathematics. pp. 458- 464 ,(1988) , 10.1007/978-3-642-37535-4_31
Agnieszka Kałamajska, ON COMPACTNESS OF EMBEDDING FOR SOBOLEV SPACES DEFINED ON METRIC SPACES Annales Academiae Scientiarum Fennicae. Mathematica. ,vol. 24, pp. 123- 132 ,(1999)
Petteri Harjulehto, Lars Diening, Michael Ruzicka, Peter Hästö, Lebesgue and Sobolev Spaces with Variable Exponents ,(2011)
David V. Cruz-Uribe, Alberto Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis ,(2013)
Przemysław Górka, Anna Macios, Almost everything you need to know about relatively compact sets in variable Lebesgue spaces Journal of Functional Analysis. ,vol. 269, pp. 1925- 1949 ,(2015) , 10.1016/J.JFA.2015.06.024
A. Fiorenza, C. Sbordone, Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$ Studia Mathematica. ,vol. 127, pp. 223- 231 ,(1998)
Humberto Rafeiro, Kolmogorov compactness criterion in variable exponent Lebesgue spaces arXiv: Functional Analysis. ,(2009)
Tomasz Adamowicz, Petteri Harjulehto, Peter Hästö, Maximal Operator in Variable Exponent Lebesgue Spaces on Unbounded Quasimetric Measure Spaces Mathematica Scandinavica. ,vol. 116, pp. 5- 22 ,(2015) , 10.7146/MATH.SCAND.A-20448
Stanislav N. Antontsev, José F. Rodrigues, On stationary thermo-rheological viscous flows Annali Dell'universita' Di Ferrara. ,vol. 52, pp. 19- 36 ,(2006) , 10.1007/S11565-006-0002-9