Tuesday, February 7, 2023 1pm to 2pm
About this Event
Fractional Leibniz rules are reminiscent of the product rule learned in calculus classes, offering estimates in the Lebesgue norm for fractional derivatives of a product of functions in terms of the Lebesgue norms of each function and its fractional derivative. We prove such estimates for Coifman-Meyer multiplier operators in the setting of Triebel-Lizorkin and Besov spaces based on quasi-Banach function spaces. As corollaries, we obtain results in weighted mixed Lebesgue spaces and Morrey spaces, where we present applications to the specific case of power weights. Other examples also include the class of rearrangement invariant quasi-Banach function spaces, of which weighted Lebesgue spaces, Lorentz spaces, and Orlicz spaces are specific examples.
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