Volumes of sub-level sets and the decay of oscillatory integrals

DOI10.7153/jmi-2021-15-54zbMath1467.32003OpenAlexW3176167306WikidataQ114012077 ScholiaQ114012077MaRDI QIDQ5000433

Ta Lê Loi

Publication date: 13 July 2021

Published in: Journal of Mathematical Inequalities (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jmi-2021-15-54

zbMATH Keywords

o-minimal structureoscillatory integralsub-level setHölder-Łojasiewicz inequality

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Real-analytic and semi-analytic sets (14P15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Inequalities for sums, series and integrals (26D15) Semialgebraic sets and related spaces (14P10) Semi-analytic sets, subanalytic sets, and generalizations (32B20)

Cites Work

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• Łojasiewicz inequalities in o-minimal structures
• Bounds of Hausdorff measures of tame sets
• Verdier and strict Thom stratifications in o-minimal structures
• On gradients of functions definable in o-minimal structures
• Geometry of subanalytic and semialgebraic sets
• Integration of oscillatory and subanalytic functions
• Stratification of families of functions definable in o-minimal structures
• Fiberwise properties of definable sets and functions in o-minimal structures
• Geometric categories and o-minimal structures
• Multidimensional van der Corput and sublevel set estimates
• Bounding the decay of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function

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