Bilinear Calderón-Zygmund operators on products of variable Hardy spaces
Let $p:\mathbb{R}^n\to (0, \infty]$ be a measurable function. Then the variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}^n)$ consists of all Lebesgue measurable functions $f$ satisfying \[ \int_{\mathbb{R}^n}|\epsilon f(x)|^{p(x)}\,dx<\infty \] for some $\epsilon\in(0,\infty)$. Moreover, for any $f\in L^{p(\cdot)}(\mathbb{R}^n)$, let \[ \|f\|_{L^{p(\cdot)}(\mathbb{R}^n)}:=\inf\left\{\lambda>0: \int_{\mathbb{R}^n} \left(\frac{|f(x)|}{\lambda}\right)^{p(x)}\,dx\le 1\right\}. \] In this paper, under some assumptions for the function $p(\cdot)$, the author obtains the boundedness of bilinear Calderón-Zygmund operators from products of variable Hardy spaces into variable Lebesgue spaces or variable Hardy spaces.
scientific article; zbMATH DE number 7039548
scientific article