info:eu-repo/semantics/article
A generalization of the boundedness of certain integral operators in variable lebesgue spaces
Fecha
2020-06Registro en:
Urciuolo, Marta; Vallejos, Lucas Alejandro; A generalization of the boundedness of certain integral operators in variable lebesgue spaces; Element D.O.O.; Journal of Mathematical Inequalities; 14; 2; 6-2020; 547-557
1846-579X
CONICET Digital
CONICET
Autor
Urciuolo, Marta
Vallejos, Lucas Alejandro
Resumen
Let n ε N. Let A1, ...Am be n×n invertible matrices. Let 0 ≤ α < n and 0 < αi < n such that α1 +...+αm = n-α . We define In [8] we obtained the boundedness of this operator from Lp(.)(Rn) into Lq(.)(Rn) for 1/q(.) = 1/p(.) - α/n, in the case that Ai is a power of certain fixed matrix A and for exponent functions p satisfying log-Hölder conditions and p(Ay) = p(y), y ε Rn. We will show now that the hypothesis on p, in certain cases, is necessary for the boundedness of Tα and we also prove the result for more general matrices Ai.