Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces

Continuous wavelet transform in variable Lebesgue spaces

In the present note we investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space. Mathematics Subject Classification (2010): Primary 42C40, Secondary 42C15, 42B08, 42A38, 46B15.

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS

Multipliers of Multidimensional Fourier Algebras

Let G be a locally compact σ-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra A(G) of G. We characterise the completely bounded multidimensional multipliers associated with A(G) in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all n-dimensional compl...

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.