Volterra Integral Operators from Campanato Spaces into General Function Spaces

Abstract

Abstract In this paper, the boundedness and compactness of embedding from Campanato spaces $$\\mathcal{L}_{p,\\lambda}$$ into tent spaces $$\\mathcal{T}_{p,s}(\\mu)$$ are investigated. As an application, we give a characterization for the boundedness of the Volterra integral operator $$J_{g}$$ from $$\\mathcal{L}_{p,\\lambda}$$ to general function spaces $$F(p,p-1-\\lambda,s)$$ . Meanwhile, the operator $$I_{g}$$ and the multiplication operator $$M_{g}$$ from $$\\mathcal{L}_{p,\\lambda}$$ to $$F(p,p-1-\\lambda,s)$$ are studied. Furthermore, the essential norm of $$J_{g}$$ and $$I_{g}$$ from $$\\mathcal{L}_{p,\\lambda}$$ to $$F(p,p-1-\\lambda,s)$$ is also considered.