Lipschitz maps and primitives for continuous functions in quasi-Banach spaces

Autor:	J. L. Ansorena, Fernando Albiac
Rok vydání:	2012
Předmět:	Discrete mathematics Continuous function Applied Mathematics Banach space Riemann integral Lipschitz continuity symbols.namesake Lipschitz domain symbols Interpolation space Metric map Birnbaum–Orlicz space Analysis Mathematics
Zdroj:	Nonlinear Analysis: Theory, Methods & Applications. 75:6108-6119
ISSN:	0362-546X
DOI:	10.1016/j.na.2012.06.016
Popis:	We show that for a wide class of non-locally convex quasi-Banach spaces X that includes the spaces l p for 0 p 1 , there exists a continuous function f : [ 0 , 1 ] → X failing to have a primitive, thus solving a problem raised by M.M. Popov in 1994. We also construct the first known examples of functions in C ( 1 ) ( [ a , b ] , X ) that fail to be Lipschitz.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::6e4b3569062261e1c94d33dd4bc56dc6 https://doi.org/10.1016/j.na.2012.06.016 Zobrazit plný text záznamu Full Text from ScienceDirect