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Currently displaying 1 – 2 of 2

Order by Relevance | Title | Year of publication

Higher integrability for maximal oscillatory Fourier integrals.

Walther, Björn Gabriel — 2001

Annales Academiae Scientiarum Fennicae. Mathematica

Estimates with global range for oscillatory integrals with concave phase

Bjorn Gabriel Walther — 2002

Colloquium Mathematicae

We consider the maximal function $| | (S^{a} f) [x] {| |}_{L^{\infty} [- 1, 1]}$ where $(S^{a} f) {(t)}^{\land} (ξ) = e^{{i t | ξ |}^{a}} f ̂ (ξ)$ and 0 < a < 1. We prove the global estimate $| | S^{a} f {| |}_{L ² (ℝ, L^{\infty} [- 1, 1])} {\leq C | | f | |}_{H^{s} (ℝ)}$ , s > a/4, with C independent of f. This is known to be almost sharp with respect to the Sobolev regularity s.

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