Functions of $L^{p}$-multipliers

OPERATOR-VALUED Lq → Lp FOURIER MULTIPLIERS

Fourier multiplier theorems provides one of the most important tools in the study of partial differential equations and embedding theorems. They are very often used to establish maximal regularity of elliptic and parabolic differential operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensively in [1, 2, 3, 5, 7, 8, 9, 10, 11, 12 ]. B...

Multipliers of Hankel transformable generalized functions

Let Hμ be the Zemanian space of Hankel transformable functions, and let H′μ be its dual space. In this paper Hμ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space O, also introduced by Zemanian, is completely characterized as the set of multipliers of Hμ and of H′μ. Certain topologies are considered on O, and continuity properties of the multiplication operation with respec...

Multipliers on Spaces of Analytic Functions

In the paper we find, for certain values of the parameters, the spaces of multipliers ( H(p, q, α), H(s, t, β) ) and ( H(p, q, α), ls ) , where H(p, q, α) denotes the space of analytic functions on the unit disc such that (1 − r)Mp(f, r) ∈ Lq( dr 1−r ). As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces. §0. Introduction. Given two sequence spaces X ...

Certain multipliers of univalent harmonic functions

Inequalities involving multipliers using the sequences {cn} and {dn} of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {cn} and {dn}, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many cases, confirm or generalize various well-kno...

FUNCTIONS ON MULTIPLIERS OF p-FOURIER ALGEBRAS