Criteria for compactness inLp-spaces,p≥ 0
作者： Veniamin G Krotov , None
DOI: 10.1070/SM2012V203N07ABEH004253
关键词: Measurable function 、 Metric space 、 Compact space 、 Bibliography 、 Mathematical Operators 、 Mathematics 、 Mathematical optimization 、 Measure (mathematics) 、 Pure mathematics 、 Smoothness (probability theory)
摘要: The paper puts forward new compactness criteria for spaces of summable and measurable functions on a metric space with measure satisfying the doubling condition. These are formulated in terms either local smoothness inequalities or maximal operators that smoothness. Bibliography: 28 titles.
harvard.edu
sci-hub.se 参考文章(21)
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)
Maurice Fréchet, Sur les ensembles compacts de fonctions mesurables Fundamenta Mathematicae. ,vol. 9, pp. 25- 32 ,(1927) , 10.4064/FM-9-1-25-32
Alberto Calderón, Ridgway Scott, Sobolev type inequalities for p>0 Studia Mathematica. ,vol. 62, pp. 75- 92 ,(1978) , 10.4064/SM-62-1-75-92
Dochun YANG, New characterizations of Haj asz-Sobolev spaces on metric spaces Science in China Series A. ,vol. 46, pp. 675- 689 ,(2003) , 10.1360/02YS0343
A. Calderón, Estimates for singular integral operators in terms of maximal functions Studia Mathematica. ,vol. 44, pp. 563- 582 ,(1972) , 10.4064/SM-44-6-563-582
Juha Heinonen, Lectures on Analysis on Metric Spaces ,(2011)
P L Ul'yanov, REPRESENTATION OF FUNCTIONS BY SERIES AND CLASSES ϕ(L) Russian Mathematical Surveys. ,vol. 27, pp. 1- 54 ,(1972) , 10.1070/RM1972V027N02ABEH001370
Masatsugu Tsuji, On the compactness of space $L^p(p>0)$ and its application to integral equations Kodai Mathematical Seminar Reports. ,vol. 3, pp. 33- 36 ,(1951) , 10.2996/KMJ/1138843067
I. A. Ivanishko, Generalized Sobolev Classes on Metric Measure Spaces Mathematical Notes. ,vol. 77, pp. 865- 869 ,(2005) , 10.1007/S11006-005-0088-X