Point-wise time-space estimates for a class of oscillatory integrals and their applications

JinMyong Kim and JinMyong An ()
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JinMyong Kim: Kim Il Sung University
JinMyong An: Kim Il Sung University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1182-1192

Abstract: Abstract This paper investigates the point-wise time-space estimates for a class of oscillatory integrals given by $$\int _{\mathbb R^{n} }e^{i \pm itP^{\frac{1}{2} } (\xi )} P^{-\frac{\alpha }{2} } (\xi )d\xi $$ ∫ R n e i ± i t P 1 2 ( ξ ) P - α 2 ( ξ ) d ξ , where P is a real non-degenerate elliptic polynomial of order $$m\ge 4$$ m ≥ 4 on $$\mathbb R^{n} $$ R n . These estimates are applied to obtain time-space integrability estimates with regularity for solutions to higher order wave-type equations.

Keywords: Oscillatory integral; Higher order wave-type equation; Point-wise time-space estimate; 42B20; 42B37; 35G10; 35B65 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-024-00589-1

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