On restricted weak-type constants of Fourier multipliers

Restricted Weak Type versus Weak Type

We prove that translation invariant multilinear operators of restricted weak type (1, 1, . . . , 1, q) must necessarily be of weak type (1, 1, . . . , 1, q). We give applications.

Weak Type Estimates for Spherical Multipliers on Noncompact Symmetric Spaces

In this paper we prove sharp weak type 1 estimates for spherical Fourier multipliers on symmetric spaces of the noncompact type. This complements earlier results of J.-Ph. Anker and A.D. Ionescu.

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS

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.

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...