Over the past fifteen years, motivated by regularity problems in evolution equations, there
has been tremendous progress in the analysis of Banach space-valued functions and …

This book deals with the theory of one-and two-parameter martingale Hardy spaces and
their use in Fourier analysis, and gives a summary of the latest results in this field. A method …

We give an elementary proof that the H p spaces over the unit disc (or the upper half plane)
are the interpolation spaces for the real method of interpolation between H 1 and H∞. This …

Given a metric measure space X, we consider a scale of function spaces T^ p, q _s (X) T sp,
q (X), called the weighted tent space scale. This is an extension of the tent space scale of …

We develop a generalized Littlewood–Paley theory for semigroups acting on Lp-spaces of
functions with values in uniformly convex or smooth Banach spaces. We characterize, in the …

We study certain interpolation and extension properties of the space of regular operators
between two Banach lattices. Let $ R_p $ be the space of all the regular (or equivalently …

Real and complex interpolation methods, when applied to the couple $({H^{{p_0}}}({E_0};{
w_0}),{H^{{p_1}}}({E_1};{w_1})) $, give what is expected if ${E_0} $ and ${E_1} $ are quasi …

We consider the problem of complex interpolation of certain Hardy-type subspaces of Köthe
function spaces. For example, suppose that X 0 and X 1 arc Köthe function spaces on the …

In this paper, we introduce a criterion for maximal operators associated with Fourier
multipliers to be bounded on L p (R d) for each p∈(1,∞). Noteworthy examples satisfying …

We establish conditions similar to the Tb theorem of David, Journé and Semmes which
guarantee the boundedness of an integral transformation T with L (X)-valued kernel on LXp …