Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces

• Autorzy: Luca Brandolini , Leonardo Colzani
• Języki publikacji: EN

Słowa kluczowe

EN

rearrangement invariant Banach function spaces; Schrödinger and wave equations; Fourier transform; multipliers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 71
• Numer: 2
• Strony: 273-286

Daty

wydano

1996

otrzymano

1996-01-03

Twórcy

autor

Luca Brandolini

• Dipartimento di Matematica, Unversità degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy

autor

Leonardo Colzani

• Dipartimento di Matematica, Unversità degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy

Bibliografia

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• [2] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
• [3] J. J. F. Fournier and J. Stewart, Amalgams of $L^p$ and $l^q$, Bull. Amer. Math. Soc. 13 (1985), 1-21.
• [4] L. Hörmander, Estimates for translation invariant operators on $L^p$ spaces, Acta Math. 104 (1960), 93-140.
• [5] C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69.
• [6] V. Lebedev and A. Olevskiĭ, $C^1$ changes of variables: Beurling-Helson type theorem and Hörmander conjecture on Fourier multipliers, Geom. Funct. Anal. 4 (1994), 213-235.
• [7] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, 1979.
• [8] W. Littman, The wave operator and $L^p$ norms, J. Math. Mech. 12 (1963), 55-68.
• [9] D. Müller and A. Seeger, Inequalities for spherically symmetric solutions of the wave equation, Math. Z. 218 (1995), 417-426.
• [10] R. S. Strichartz, Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714.
• [11] P. Szeptycki, Some remarks on the extended domain of Fourier transform, Bull. Amer. Math. Soc. 73 (1967), 398-402.