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Estimates for Hyperbolic Equations of Space Dimension 3 by Mitsuru Sugimoto is a Mathematics article available to read on EtoBox.

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We discuss the problem of boundedness from L p (R n ) to L p$ (R n ) (1Âp+1Âp$=1, 1 p 2) of operators of the type M=F &1 e i.(!) a(!) F, which is related to the study of hyperbolic equations with constant coefficients. The boundedness is dependent on a geometrical property of 7=. &1 (1), and its dependence has been exactly determined in the cases n=2, 1 p 2 and n 3, p=1, 2 (M. Sugimoto, Math. Z. 215 (1994), 519 531; 222 (1996), 521 531). This paper is devoted to the unsolved case 1<p<2, and a strange phenomenon is exhibited in the simplest case n=3. ## 1998 Academic Press Here P(D t , D x ) is a homogeneous constant coefficient partial differential operator of degree m in the time t and the space x # R n , which is strictly article no.

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Author

Mitsuru Sugimoto

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

1998

Language

EN

Field

Mathematics (Physical Sciences)