On $$L^p$$ L p -Boundedness of Pseudo-Differential Operators of Sjöstrand’s Class

On $$L^p$$ L p -Boundedness of Pseudo-Differential Operators of Sjöstrand’s Class We extended the known result that symbols from modulation spaces $$M^{\infty ,1}(\mathbb {R}^{2n})$$ M ∞ , 1 ( R 2 n ) , also known as the Sjöstrand’s class, produce bounded operators in $$L^2(\mathbb {R}^n)$$ L 2 ( R n ) , to general $$L^p$$ L p boundedness at the cost of loss of derivatives. Indeed, we showed that pseudo-differential operators acting from $$L^p$$ L p -Sobolev spaces $$L^p_s(\mathbb {R}^n)$$ L s p ( R n ) to $$L^p(\mathbb {R}^n)$$ L p ( R n ) spaces with symbols from the modulation space $$M^{\infty ,1}(\mathbb {R}^{2n})$$ M ∞ , 1 ( R 2 n ) are bounded, whenever $$s\ge n|1/p-1/2|.$$ s ≥ n | 1 / p - 1 / 2 | . This estimate is sharp for all $$1< p<\infty $$ 1 < p < ∞ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Fourier Analysis and Applications Springer Journals

On $$L^p$$ L p -Boundedness of Pseudo-Differential Operators of Sjöstrand’s Class

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Springer US
Copyright © 2016 by Springer Science+Business Media New York
Mathematics; Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics
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