Extensions and Approximations

Ikemefuna Agbanusi

Published 2023-08-26Version 1

We investigate the order of approximation when certain singular kernels when act on the zero-extension of functions. The results can be repurposed to give non trivial estimates on the moduli of continuity of zero-extensions. Our approach avoids the use of Hardy type inequalities and so applies to any function in $L^p([0,1]^d)$ regardless of smoothness.