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

Luca Brandolini; Leonardo Colzani

Colloquium Mathematicae (1996)

  • Volume: 71, Issue: 2, page 273-286
  • ISSN: 0010-1354

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Brandolini, Luca, and Colzani, Leonardo. "Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces." Colloquium Mathematicae 71.2 (1996): 273-286. <http://eudml.org/doc/210441>.

@article{Brandolini1996,
author = {Brandolini, Luca, Colzani, Leonardo},
journal = {Colloquium Mathematicae},
keywords = {rearrangement invariant Banach function spaces; Schrödinger and wave equations; Fourier transform; multipliers; rearrangement invariant Banach function space},
language = {eng},
number = {2},
pages = {273-286},
title = {Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces},
url = {http://eudml.org/doc/210441},
volume = {71},
year = {1996},
}

TY - JOUR
AU - Brandolini, Luca
AU - Colzani, Leonardo
TI - Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 2
SP - 273
EP - 286
LA - eng
KW - rearrangement invariant Banach function spaces; Schrödinger and wave equations; Fourier transform; multipliers; rearrangement invariant Banach function space
UR - http://eudml.org/doc/210441
ER -

References

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  2. [2] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988. Zbl0647.46057
  3. [3] J. J. F. Fournier and J. Stewart, Amalgams of L p and l q , Bull. Amer. Math. Soc. 13 (1985), 1-21. 
  4. [4] L. Hörmander, Estimates for translation invariant operators on L p spaces, Acta Math. 104 (1960), 93-140. Zbl0093.11402
  5. [5] C. E. Kenig, G. Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), 33-69. Zbl0738.35022
  6. [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. Zbl0798.42004
  7. [7] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, 1979. Zbl0403.46022
  8. [8] W. Littman, The wave operator and L p norms, J. Math. Mech. 12 (1963), 55-68. Zbl0127.31705
  9. [9] D. Müller and A. Seeger, Inequalities for spherically symmetric solutions of the wave equation, Math. Z. 218 (1995), 417-426. Zbl0828.35072
  10. [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. Zbl0372.35001
  11. [11] P. Szeptycki, Some remarks on the extended domain of Fourier transform, Bull. Amer. Math. Soc. 73 (1967), 398-402. Zbl0166.09903

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