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Global and local regularity of fourier integral operators on weighted and unweighted spaces / David Dos Santos Ferreira, Wolfgang Staubach.
- Format:
- Book
- Author/Creator:
- Ferreira, David Dos Santos, 1975- author.
- Staubach, Wolfgang, 1970- author.
- Series:
- Memoirs of the American Mathematical Society ; Volume 229, Number 1074.
- Memoirs of the American Mathematical Society, 1947-6221 ; Volume 229, Number 1074
- Language:
- English
- Subjects (All):
- Fourier integral operators.
- Mathematical analysis.
- Physical Description:
- 1 online resource (86 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 2013.
- Language Note:
- English
- Summary:
- The authors investigate the global continuity on $L^p$ spaces with $p\in [1,\infty]$ of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global $L^2$ boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hormander class amplitudes i.e. those in $S^{m} _{\varrho, \delta}$ with $\varrho, \delta \in [0,1]$. They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted $L^{p}$ spaces, $L_{w}^p$ with $1
- Contents:
- ""Chapter 3. Global and Local Weighted ^{ } Boundedness of Fourier Integral Operators""""3.1. Tools in proving weighted boundedness""; ""3.2. Counterexamples in the context of weighted boundedness""; ""3.3. Invariant formulation in the local boundedness""; ""3.4. Weighted local and global ^{ } boundedness of Fourier integral operators""; ""Chapter 4. Applications in Harmonic Analysis and Partial Differential Equations""; ""4.1. Estimates in weighted Triebel-Lizorkin spaces""; ""4.2. Commutators with BMO functions""; ""4.3. Applications to hyperbolic partial differential equations""
- ""Bibliography""
- Notes:
- "Volume 229, Number 1074 (first of 5 numbers)."
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 1-4704-1528-3
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