G. Bourdaud

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20182024

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math.FA2024

The higher order chain rule in Sobolev spaces

Gérard Bourdaud

We establish the Faà di Bruno formula, in the sense of almost everywhere equality, for derivatives of the composed function $f \circ g$ , for all function $f : R \to R$ such…

math.FA2022

An introduction to composition operators in Sobolev spaces

Gérard Bourdaud

We propose a survey on composition operators in classical Sobolev spaces. We mention results obtained in 2019, on the continuity of such operators.

math.FA2021

Szasz's theorem and its generalizations

Gérard Bourdaud

We establish the most general Szasz type estimates for homogeneous Besov and Lizorkin-Triebel spaces, and their realizations.

math.FA2018

Continuity of composition operators in Sobolev spaces

Gérard Bourdaud, Madani Moussai

We prove that all the composition operators $T_{f} (g) := f \circ g$ , which take the Adams-Frazier space $W_{p}^{m} \cap W ˙_{m p}^{1} (R^{n})$ to itself, are continuous mapping…