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Some Lp(L)– and L2(L2)– estimates for oscillatory Fourier transforms

  • Björn G. Walther
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Let \(\begin{gathered} 0 \leqslant {{n}_{k}} \leqslant {{p}_{k}}, 0 \leqslant {{m}_{k}} < {{q}_{k}}, 0 \leqslant {{x}_{k}} < {{p}_{k}},0 \leqslant {{y}_{k}} < {{q}_{k}}, \hfill \\ \left( {{{S}^{a}}f} \right){{\left( t \right)}^{ \wedge }} = {\text{exp}}\left( {it{{{\left| \xi \right|}}^{a}}} \right)\hat{f}\left( \xi \right) \hfill \\ \end{gathered} \). We discuss some examples of maximal estimates and weighted L2-estimates for Sf. The techniques used include asymptotics for Bessel functions and the complete orthogonal decomposition of L2(ℝ n ) using spherical harmonics.

Keywords

Spherical Harmonic Maximal Function Pointwise Convergence Schrodinger Equation Maximal Estimate 
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Copyright information

© Birkhäuser Boston 1999

Authors and Affiliations

  • Björn G. Walther

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