Some remarks on the Banach space valued Hilbert transform

On the character space of Banach vector-valued function algebras

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

Hilbert Space-valued Mixingales

Some Personal Remarks on the Radon Transform

Back in 1955, I worked on extending the mean value theorem of Leifur Ásgeirsson [1937] for the ultrahyperbolic equation on Rn ×Rn to Riemannian homogeneous spaces G/K ×G/K. I was motivated by Godement’s generalization [1952] of the mean value theorem for Laplace’s equation Lu = 0 to the system Du = 0 for all G-invariant differential operators D (annihilating the constants) on G/K. At the time (...

Some Remarks on the Differential Transform Method

The differential transform method and Herrera’s complex integral method are shown to be related through the Taylor-Cauchy transform, which appears as a genuine fore-runner of both methods. A short discussion of this result is provided. Mathematics Subject Classification: 34A05, 34A25, 34A30, 34A34, 35C10

Convolution Operators on Banach Space Valued Functions.

The purpose of this paper is to obtain systematically certain classical inequalities concerning the Hilbert transform, the function g of Littlewood and Paley, their generalizations to several variables, and related results.t This we accomplish by establishing certain inequalities for convolution operators on Banach space valued functions. Given a Banach space B, If I will denote the norm of the...