$\Psi $-pseudodifferential operators and estimates for maximal oscillatory integrals
Volume 183 / 2007
Studia Mathematica 183 (2007), 249-258
MSC: Primary 35S05; Secondary 42B20, 42B20.
DOI: 10.4064/sm183-3-3
Abstract
We define a class of pseudodifferential operators with symbols $a(x,\xi )$ without any regularity assumptions in the $x$ variable and explore their $L^{p}$ boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.
