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Pseudodifferential Operators with Rough Symbols by Stefanov, Atanas is a scholarly article available to read on EtoBox.

What is Pseudodifferential Operators with Rough Symbols about?

In this work, we develop $L^p$ boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the $x$ variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in terms of scale invariant quantities involving the symbols. All the estimates are shown to be sharp with respect to the required smoothness in the $\xi$ variable. As a corollary, we obtain $L^p$ bounds for (smoothed out versions of) the maximal directional Hilbert transform and the Carleson operator.

Author

Stefanov, Atanas

Published

2007

Language

EN