2026 CMS Winter Meeting
Montreal, Dec 11 - 14, 2026
Harmonic Analysis and Geometric Measure Theory
Org: Juyoung Lee, Nikou Lei and Blanca Radillo--Murguia (University of British Columbia)
Org: Juyoung Lee, Nikou Lei and Blanca Radillo--Murguia (University of British Columbia)
- MENGMENG DOU, University of British Columbia
Regularity of multi-parameter Fourier integral operators [PDF]
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We investigate a new class of Fourier integral operators ${\bf F}$ defined in $\mathbb R^{\bf N}$. Their symbols are allowed to satisfy a differential inequality with certain multi-parameter characteristic. We prove these operators of order $-{{\bf N}-1\over 2}$ bounded from the classical, atom decomposable $H^1$-Hardy space to $L^1(\mathbb R^{\bf N})$. As a result, we obtain a sharp $L^p$-estimate.
Simultaneously, a generalized Sobolev $L^p$-space is introduced. We establish the Sobolev $L^p$-norm inequality for convolutions with a distribution having singularity on the unit sphere. As an application, we give new a priori estimate for the solution of wave equations by requiring less regularity on the source term and initial data.
- MARCO FRACCAROLI, University of Massachusetts Lowell
- ROBERT FRASER, Wichita State University
- KAIWEN JIN, University of Wisconsin-Madison
- JORIS ROOS, University of Massachusetts Lowell
- HRIT ROY, University of Jyväskylä
- IGNACIO URIARTE-TUERO, University of Toronto
- YUFEI ZHAN, University of Pennsylvania
- ROBERT FRASER, Wichita State University