continuity of pseudo-differential operators with discontinuous symbol
Authors: J. Alvarez and R. Durán
Journal: Proc. Amer. Math. Soc. 104 (1988), 165-168
MSC: Primary 42B20; Secondary 42B10, 47B05
MathSciNet review: 958060
Abstract: A set is called conic if implies , for all .
In localizing a partial differential equation, the following question arose: Let us consider a pseudo-differential operator whose symbol is the characteristic function of a conic subset of . Will be a bounded operator in ?
We present as a counterexample a pseudo-differential operator whose symbol is the characteristic function of a conic subset of , which is unbounded on for .
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Keywords: Conic set, pseudo-differential operator, Hilbert transform over a curve
Article copyright: © Copyright 1988 American Mathematical Society