caa a22 4500 467931720 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060901xx s 000 0 eng 10.1007/s00020-005-1411-3 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1411-3 A Class of Integral Operators on the Unit Ball of$$\mathbb{C}^{n}$$ [Elektronische Daten] [Osman Kures, Kehe Zhu] Abstract.: For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator $$ Tf(z) = {\left( {1 - |z|^{2} } \right)}^{a} {\int_{\mathbb{B}_{n} } {\frac{{{\left( {1 - |w|^{2} } \right)}^{b} }} {{{\left( {1 - \langle z,w\rangle } \right)}^{c} }}f(w)\;dv(w)} } $$ is bounded on $$L^{p} {\left( {\mathbb{B}_{n} ,\;dv_{t} } \right)},$$ where $$\mathbb{B}_{n}$$ is the open unit ball in $$\mathbb{C}^{n} ,\;1 \leq p < \infty ,$$ and dvt (z)=(1 − |z| 2) tdv (z) with dv being volume measure on $$\mathbb{B}_{n} .$$ The characterization remains the same if we replace (1 − 〈z,w 〉) c in the integral kernel above by its modulus |1 − 〈z,w〉| c. Birkhäuser Verlag, Basel, 2006 Kures Osman Department of Mathematics, State University of New York, 12222, Albany, NY, USA aut Zhu Kehe Department of Mathematics, State University of New York, 12222, Albany, NY, USA aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 56/1(2006-09-01), 71-82 0378-620X 56:1<71 2006 56 20 https://doi.org/10.1007/s00020-005-1411-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1411-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kures Osman Department of Mathematics, State University of New York, 12222, Albany, NY, USA aut NATIONALLICENCE 700 1- Zhu Kehe Department of Mathematics, State University of New York, 12222, Albany, NY, USA aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 56/1(2006-09-01), 71-82 0378-620X 56:1<71 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer