On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball

We introduce the following integral-type operator on the space H(B)H(B) of all holomorphic functions on the unit ball B⊂CnB⊂CnPφg(f)(z)=∫01f(φ(tz))g(tz)dtt,z∈B, where g∈H(B)g∈H(B), g(0)=0g(0)=0 and φ   is a holomorphic self-map of BB. The boundedness and compactness of the operator from the Bloch space BB or the little Bloch space B0B0 to the Bloch-type space BμBμ or the little Bloch-type space Bμ,0Bμ,0, are characterized. In the main results we calculate the essential norm of the operators Pφg:B(or B0)→Bμ(or Bμ,0) in an elegant way.