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Multidimensional decay in the van der Corput lemma

100%

Ruzhansky M.

Studia Mathematica

2012

tom 208

nr 1

1-10

We establish a multidimensional decay of oscillatory integrals with degenerate stationary points, gaining the decay with respect to all space variables. This bridges the gap between the one-dimensional decay for degenerate stationary points given by the classical van der Corput lemma and the multidimensional decay for non-degenerate stationary points given by the stationary phase method. Complex-valued phase functions as well as phases and amplitudes of limited regularity are considered. Conditions for estimates to be uniform in parameter are also given.

Recent progress in the regularity theory of Fourier integrals with real and complex phases and solutions to partial differential equations

100%

Ruzhansky M.

Banach Center Publications

2003

tom 60

nr 1

151-160

In this paper we will give a brief survey of recent regularity results for Fourier integral operators with complex phases. This will include the case of real phase functions. Applications include hyperbolic partial differential equations as well as non-hyperbolic classes of equations. An application to an oblique derivative problem is also given.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Ruzhansky M.

1 2012

1 2003

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Multidimensional decay in the van der Corput lemma

Recent progress in the regularity theory of Fourier integrals with real and complex phases and solutions to partial differential equations