Peral, Juan C. \(L^p\) estimates for the waves equation. (English) Zbl 0442.35017 J. Funct. Anal. 36, 114-145 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 65 Documents MSC: 35B45 A priori estimates in context of PDEs 35L05 Wave equation 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:estimates; wave equation; initial conditions; Klein-Gordon equation; convolution against the kernel PDF BibTeX XML Cite \textit{J. C. Peral}, J. Funct. Anal. 36, 114--145 (1980; Zbl 0442.35017) Full Text: DOI References: [1] Alfors, L.V., Complex analysis, (1953), McGraw-Hill New York [2] Brenner, On Lp → lp′ estimates for the wave equation, Math. Z., (1975) [3] Brenner, Lp → lp′ estimates for F.I.O. related to hyperbolic equations, Math. Z., (1977) [4] Chazarin, Opérateurs hyperboliques, Ann. inst. Fourier (Grenoble), 24, (1974) [5] Courant-Hilbert, Methods of mathematical physics, (1962), Interscience New York · Zbl 0099.29504 [6] Egorov, On canonical transformations, Uspehi mat. nauk, 25, (1969) [7] Fefferman, Inequalities for strongly singular convolution operators, Acta math., 124, (1970) · Zbl 0188.42601 [8] Fefferman-Stein, Hp spaces of several variables, Acta math., 129, (1972) · Zbl 0257.46078 [9] Hadamard, Le problème de Cauchy et LES équations hyperboliques, (1932), Hermann Paris · Zbl 0006.20501 [10] Hirchmann, Multiplier transformations, Duke math. J., 26, (1956) [11] Hörmander, L., Fourier integral operators, Acta math., 127, (1971) · Zbl 0212.46601 [12] Hörmander, L., Prospect in math., Ann. of math., 70, (1971) [13] Ishii, On some Fourier multipliers, Math. japon., 3, (1974) · Zbl 0321.35022 [14] Lax, Asymptotic solutions of oscillatory initial value problems, Duke math. J., 24, (1957) · Zbl 0083.31801 [15] Littman, The wave equation, J. math. mech., 12, (1963) · Zbl 0127.31705 [16] Ludwig, Exact and asymptotic solutions of the Cauchy problem, Comm. pure appl. math., 13, (1960) · Zbl 0098.29601 [17] Mizohata-Ohya, Sur la condition d’hyperbolicité, Japan. J. math., 40, (1971) · Zbl 0231.35048 [18] Riesz, L’intégral de Riemann-lioville et le problème de Cauchy, Acta math., 81, (1950) [19] Stein, Lp boundedness of certain convolution operators, Bull. amer. math. soc., 77, (1971) · Zbl 0217.44503 [20] Stein, Interpolation of linear operators, Trans. amer. math. soc., 83, (1956) · Zbl 0072.32402 [21] Stein, Singular integrals and differentiability properties of functions, (1970), Princeton Univ. Press Princeton, N.J · Zbl 0207.13501 [22] Stein, Singular integrals, () · Zbl 0576.42017 [23] Stein-Weiss, Introduction to Fourier analysis on Euclidean spaces, (1971), Princeton Univ. Press Princeton, N.J · Zbl 0232.42007 [24] Strichartz, Convolutions with kernels having singularities over a sphere, Trans. amer. math. soc., 148, (1970) · Zbl 0199.17502 [25] Wainger, Special trigonometric series in K-dimensions, Mem. amer. math., 59, (1965) · Zbl 0136.36601 [26] Watson, Theory of Bessel function, (1941), Cambridge Univ. Press London/New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.