Operating functions on Fourier multipliers

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS

The Functions Operating on Certain Algebras of Multipliers

In this note, we announce a new result concerning functions operating on multiplier algebras. We begin by introducing the following notation. Let G be a LCA group with dual group I\ M(G) will denote the algebra of finite, regular Borel measures on G. Let M0(G) = {M E M(G)\ jl vanishes at <*> on T}. If 1 < p < °°, let M (G) denote the class of multiplier transformations on L (G). If T G Mp(G), f...

Maximal Functions Associated with Fourier Multipliers of Mikhlin-hörmander Type

We show that maximal operators formed by dilations of Mikhlin-Hörmander multipliers are typically not bounded on L(R). We also give rather weak conditions in terms of the decay of such multipliers under which L boundedness of the maximal operators holds.

Square Functions and Maximal Operators Associated with Radial Fourier Multipliers

where (Pt)t>0 is an approximation of the identity defined by the dilates of a ‘nice’ kernel (for example (Pt) may be the Poisson or the heat semigroup). Their significance in harmonic analysis, and many important variants and generalizations have been discussed in Stein’s monographs [38], [39], [44], in the survey [45] by Stein and Wainger, and in the historical article [43]. Here we focus on L...

Multipliers on Modules Over the Fourier Algebra

Let G be an infinite compact group and G its dual. For 1< p < oom P(G) is a module over 21(G) A(G), the Fourier algebra of G. For 1 < p, q < o0, let Ip q = HomA(G)( P(G), ?'(G)). If G is abelian, then Jll is the space of LP(G)-multipliers. For 1 < p < 2 and p the conjugate index of p, A(G) -1,1 p,p p, p 2, 2 (G). Further, the space ll is the dual of a space called d p a subspace of eo(G). Using...