Oliver Dragicevic -- Sharp L^p asymptotics for powers of the complex Riesz transform

Author information

• Oliver Dragicevic
• University of Ljubljana, Slovenia

Abstract:

Let R_1,R_2 be the Riesz transforms on the complex plane. The singular integral R=R_2+iR_1 is called the complex Riesz transform. We establish the estimates on \(L^p\), \(1 < p < \infty\) for the integer powers \(R^k\) of \(R\) that are sharp simultaneously in \(k\) and \(p\). This answers a question suggested in a 1996 work by Iwaniec and Martin. We present three different proofs of this result. We also conjecture the exact values of the \(L^p\) norms of \(R^k\). This is a joint work with Andrea Carbonaro and Vjekoslav Kovac.

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