We consider a singular an integral operator K with a variable Calderon-Zygmund type kernel k(x:xi), x is an element of R-n, xi is an element of R-n\{0}, satisfying a mixed homogeneity condition of the form k(x:mu(n1)xi(1),...,mu(alpha n)xi(n)) = mu(-)Sigma(n)(i=1) (alpha i) k(x:xi), alpha 1 >= 1 and mu > 0. The continuity of this operator in L-p(R-n) is well studied by Fabes and Riviere. Our goal is to extend their result to generalized Morrey spaces L-p,L-w(R-n), p is an element of (1, infinity) with a weight w satisfying suitable dabbling and integral conditions. A special attentional is paid to the commutator L[a, k] = Ka-aK with the operator of multiplication by BMO functions.

Singular integrals and commutators in generalized Morrey spaces

SOFTOVA, Lyoubomira
2006

Abstract

We consider a singular an integral operator K with a variable Calderon-Zygmund type kernel k(x:xi), x is an element of R-n, xi is an element of R-n\{0}, satisfying a mixed homogeneity condition of the form k(x:mu(n1)xi(1),...,mu(alpha n)xi(n)) = mu(-)Sigma(n)(i=1) (alpha i) k(x:xi), alpha 1 >= 1 and mu > 0. The continuity of this operator in L-p(R-n) is well studied by Fabes and Riviere. Our goal is to extend their result to generalized Morrey spaces L-p,L-w(R-n), p is an element of (1, infinity) with a weight w satisfying suitable dabbling and integral conditions. A special attentional is paid to the commutator L[a, k] = Ka-aK with the operator of multiplication by BMO functions.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4701533
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 49
  • ???jsp.display-item.citation.isi??? 48
social impact