A note on k-plane integral transforms

A note on the comparison between Laplace and Sumudu transforms

k-PLANE TRANSFORMS AND RELATED OPERATORS ON RADIAL FUNCTIONS

We prove sharp mixed norm inequalities for the k-plane transform when acting on radial functions and for potential-like operators supported in k-planes. We also study the Hardy-Littlewood maximal operator on k-planes for radial functions for which we obtain a basic pointwise inequality with interesting consequences. §

A note on $lambda$-Aluthge transforms of operators

Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...

- L q estimates for generalized k - plane transforms Philip

In this paper, optimal Lp − Lq estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the k-plane transform. An important advance over previous work (e.g., [9]) is that full Lp − Lq estimates are obtained by methods which have traditionally yielded only restricted weak-type estimates. In the process, one is lead to make coercivity estimates for c...

SOME INTEGRAL TRANSFORMS OF THE GENERALIZED k-MITTAG-LEFFLER FUNCTION

In the paper, the authors generalize the notion “k-Mittag-Leffler function”, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function. 1. Preliminaries Throughout this paper, let C, R, R0 , R, Z − 0 , and N denote respectively the sets of com...