Singular integrals with variable kernel and fractional differentiation in homogeneous Morrey-Herz-type Hardy spaces with variable exponents

Abstract

Let T be the singular integral operator with variable kernel defined by Tf(x)=p.v.∫RnΩ(x,x−y)|x−y|nf(y)dy$$\begin{array}{} \displaystyle Tf(x)= p.v. \int\limits_{\mathbb{R}^{n}}\frac{{\it\Omega}(x,x-y)}{|x-y|^{n}}f(y)\text{d}y \end{array} $$

Keywords

• variable kernel
• fractional differentiation
• sobolev spaces iγ(bmo)
• morrey-herz-type hardy space with variable exponents
• 42b20
• 42b25
• 42b35