Extension of Fourier $L\sp{p}―L\sp{q}$ multipliers

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...

Lévy processes and Fourier multipliers

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1 < p < ∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.

Stable Sampling and Fourier Multipliers

We study the relationship between stable sampling sequences for bandlimited functions in Lp(Rn) and the Fourier multipliers in Lp. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship. 2010 Mathematics Subject Classification: 42A45, 42B15, 42C15, 62...

Fourier Multipliers and Dirac Operators

We use Fourier multipliers of the Dirac operator and Cauchy transform to obtain composition theorems and integral representations. In particular we calculate the multiplier of the Π-operator. This operator is the hypercomplex version of the Beurling Ahlfors transform in the plane. The hypercomplex Beuling Ahlfors transform is a direct generalization of the Beurling Ahlfors transform and reduces...

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS