Sine and cosine equations on commutative hypergroups
In this paper we describe the solutions of the functional equations expressing the addition theorems for sine and cosine on commutative hypergroups.
math.FA↗
arXiv subjects
László Székelyhidi
Publications and source records attributed to László Székelyhidi.
The $L^p-$Operator Norm of a Quadratic Perturbation of the Real Part of the Ahlfors--Beurling Operator
We will explain how to compute the exact $L^p$ operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a new approach of constructing a sequence of laminates (probability measures for which Jensen's inequality holds, but for rank one concave functions) to give an almost extremal sequence to approximate the operator. The upper bound estimate is given by extending the estimates of the quadratic perturbation of the martingale transform to continuous martingales. The use of "heat martingales" then allow us to connect the Riesz transforms to the continuous martingale estimate.
math.AP↗