Weighted Hardy–Littlewood Spacesin Piecewise Smooth Domains

New weighted spaces of the Hardy–Littlewood type of continuous functions defined in domains with piecewise smooth boundaries are introduced, and their structural properties are described. It is established that these spaces contain functions representable by generalized integrals of the Cauchy type with homogeneous kernels of degree $$-1 $$ . The latter circumstance opens up the possibility of using these spaces for solving elliptic systems of the first and second order with continuous coefficients.