IJPAM: Volume 41, No. 4 (2007)

VECTOR-VALUED SINGULAR INTEGRAL OPERATORS ON
THE PRODUCT SPACES $H^{1}$ AND $BMO$

Luiz Antonio Pereira Gomes$^1$, Eduardo Brandani da Silva$^2$
$^{1,2}$Department of Mathematics
Maringa State University - UEM
Av. Colombo 5790, Maringá, PR 87020-900, BRAZIL
$^1$e-mail: lapgomes@uem.br
$^2$e-mail: ebsilva@wnet.com.br


Abstract.Conditions for boundedness of singular vector integral operators on Benedek-Panzone spaces $L^P=L^{p_2}(L^{p_1})$ with mixed norms for $1 < P, \, p_1 , \, p_2 < \infty$ are know in the literature. We shall concern here with the limiting cases of integral operators in $(H^1,L^1)$ and $(L^{\infty},BMO)$, where $H^1$ and $BMO$ are spaces in the product case.

Received: November 22, 2007

AMS Subject Classification: 42B30, 46E40, 47B38

Key Words and Phrases: product spaces, singular integral operators, vector-valued operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 4