Boundedness of the sub-linear operators for non-doubling measure. (English) Zbl 1199.47161
Summary: In this paper, we discuss the boundedness of operators under a growth condition on the Radon measure \(\mu\) on \(\mathbb{R}^d\), which may be non-doubling. We obtain some results on the boundedness of sublinear operators on Herz spaces for a non-doubling measure with \(L^q\) boundedness. These results generalize the same conclusions for doubling measures.
MSC:
47B38 | Linear operators on function spaces (general) |
42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
42B30 | \(H^p\)-spaces |