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Results tagged with convolution
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user 479798
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Does convolution with $(1+|x|)^{-n}$ define an operator $L^p(\mathbb R^n) \to L^p(\mathbb R^n)$
By Young's convolution inequality, this would define a bounded mapping $L^p(\mathbb R^n) \to L^p(\mathbb R^n)$.
Unfortunately, $( 1 + |x| )^{-n}$ is not integrable. … I am aware of some mapping theorems for Lorentz spaces, and I think that convolution with $( 1 + |x| )^{-n}$ defines a mapping between Lorentz spaces. …
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