Estimates with global range for oscillatory integrals with concave phase
Tom 91 / 2002
Colloquium Mathematicum 91 (2002), 157-165
MSC: 42A45, 42B08, 42B25.
DOI: 10.4064/cm91-2-1
Streszczenie
We consider the maximal function where (S^af) (t)^\wedge (\xi) = e ^ {i t |\xi| ^ a} \widehat f(\xi) and 0 < a < 1. We prove the global estimate \| {S ^ a f}\|_ {L ^ 2 (\mathbb R , L ^ \infty [ -1 , 1 ])} \leq C \| f \| _{H^ s(\mathbb R)}, \quad\ s > a/4, with C independent of f. This is known to be almost sharp with respect to the Sobolev regularity s.
