Fourier multipliers of generalized Lipschitz spaces

Multipliers of generalized frames in Hilbert spaces

multipliers of generalized frames in hilbert spaces

Commutators for Fourier multipliers on Besov Spaces

The mapping properties of commutators [T,M ] = TM −MT , for operators between function spaces, and their various generalizations play an important role in harmonic analysis, PDE, interpolation theory and other related areas. A typical situation arises when M = Mb is the pointwise multiplication by a function b and T is a Calderón–Zygmund operator on R. Then well– known results of A.P. Calderón ...

Fourier Multipliers on Weighted L-spaces

In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type (p, p) on Lp(Rn) if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery’s result is sharp in a certain sense. We also obtain a weighted analogue of Carbery’s result. Some applications of our results are also given.

Biseparating Maps on Generalized Lipschitz Spaces

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F -valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uni...