All Questions

While reading this article on near $L^1$ estimates for the spherical lacunary maximal function, I came across the estimate $$ |\partial^{\gamma} (\widetilde{\sigma} \ast \sigma)(x)| \lesssim |x|^{-(1 +...

Suppose that $f : \mathbb R^n \to \mathbb R^n$ is a locally integrable function. I am interested in the integral $$ x \to \int_{\mathbb R^n} ( 1 + |y| )^{-n} f(x-y) \;dy $$ If the decay of the ...

Suppose $G$ is a locally compact abelian Hausdorff group (LCA), and $\lambda$ is the Haar measure on it. We all know the convolution of two $L^1(\lambda)$ functions $f$ and $g$ on $G$ is defined as $$...