Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type
SPEAKER | Lesley Ward
DATE | May 12(Fri), 2017
TIME | 11:00
PLACE | 1503
ABSTRACT | Much effort has been devoted to generalizing the Calder?n-Zygmund theory from Euclidean spaces to metric measure spaces, or spaces of homogeneous type. Here the underlying space ?nRn with Euclidean metric and Lebesgue measure is replaced by a set XX with a general metric or quasi-metric and a doubling measure. Further, one can replace the Laplacian operator that underpins the Calder?n-Zygmund theory by more general operators LL satisfying heat kernel estimates. I will present recent joint work with P. Chen, X.T. Duong, J. Li and L.X. Yan along these lines. We develop the theory of product Hardy spaces HpL1,L2(X1¡¿X2)HL1,L2p(X1¡¿X2), for 1¡Âp<¡Ä1¡Âp<¡Ä, defined on products of spaces of homogeneous type, and associated to operators L1L1, L2L2 satisfying Davies-Gaffney estimates. This theory includes definitions of Hardy spaces via appropriate square functions, an atomic Hardy space, a Calder?n-Zygmund decomposition, interpolation theorems, and the boundedness of a class of Marcinkiewicz-type spectral multiplier operators.