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A priori estimates for the wave equation and some applications. (English) Zbl 0189.40701


MSC:

35L05 Wave equation

Citations:

Zbl 0199.17502
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Full Text: DOI

References:

[1] Aronszajn, N.; Adams, R.; Smith, K. T., Theory of Bessel potentials, part II, Ann. Inst. Fourier (Grenoble), 17, 136 (1967) · Zbl 0185.19703
[2] Bers, L.; John, F.; Schechter, M., Partial Differential Equations (1964), Interscience: Interscience New York · Zbl 0126.00207
[3] Calderón, A. P., Lebesgue Spaces of Differentiable Functions and Distributions, (Symposium on Pure Math., 5 (1961)), 33-49 · Zbl 0195.41103
[4] Hörmander, L., Linear Partial Differential Operators (1964), Springer Pub: Springer Pub New York
[5] Hörmander, L., Estimates for translation invariant operators in \(L^p\) spaces, Acta. Math., 104, 93-140 (1960) · Zbl 0093.11402
[6] Lax, P. D.; Phillips, R. S., Scattering Theory (1967), Academic Press: Academic Press New York · Zbl 0214.12002
[7] Littman, W., The wave operator and \(L^p\) norms, J. Math. Mech., 12, 55-68 (1963) · Zbl 0127.31705
[8] Littman, W., Multipliers in \(L^p\) and interpolation, Bull. Amer. Math. Soc., 71, 764-766 (1965) · Zbl 0156.36504
[9] Nelson, S., Asymptotic Behavior of Certain Fundamental Solutions of the Klein-Gordon Equation, (Thesis (1966), M.I.T: M.I.T Cambridge, Massachusetts 02159)
[10] Seeley, R. T., Singular integrals and boundary value problems, Amer. J. Math., 88, 781-809 (1966) · Zbl 0178.17601
[11] Segal, I., Quantization and Dispersion for Non-linear Relativistic Equations, (Proceedings of the Conference on the Mathematical Theory of Elementary Particles (1966), M.I.T. Press: M.I.T. Press Cambridge, Mass), 79-108
[12] Stein, E. M., The characterization of functions arising as potentials, I, Bull. Amer. Math. Soc., 67, 102-104 (1961) · Zbl 0127.32002
[13] Stein, E. M., The characterization of functions arising as potentials, II, Bull. Amer. Math. Soc., 68, 577-582 (1962)
[14] Strauss, W. A., Decay and asymptotics for \(u = F(u)\), J. Func. Anal., 2, 409-457 (1968) · Zbl 0182.13602
[15] Strichartz, R., Convolutions with kernels having singularities on a sphere, Trans. Amer. Math. Soc. (1970), to appear · Zbl 0199.17502
[16] Strichartz, R., Multipliers on Fractional Sobolev Spaces, J. Math. Mech., 16, 1031-1060 (1967) · Zbl 0145.38301
[17] Taibleson, M., On the theory of Lipschitz spaces of distributions on Euclidean \(n\)-space I, J. Math. Mech., 13, 407-479 (1964) · Zbl 0132.09402
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