| Title:
|
A class of integral operators on mixed norm spaces in the unit ball (English) |
| Author:
|
Li, Songxiao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
1013-1023 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball. (English) |
| Keyword:
|
integral operator |
| Keyword:
|
mixed norm space |
| Keyword:
|
boundedness |
| MSC:
|
30H05 |
| MSC:
|
32A36 |
| MSC:
|
47B35 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1174.47349 |
| idMR:
|
MR2356936 |
| . |
| Date available:
|
2009-09-24T11:51:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128222 |
| . |
| Reference:
|
[1] A. Benedek and R. Panzone: The spaces $L^p$ with mixed norm.Duke Math. J. 28 (1961), 301–324. MR 0126155, 10.1215/S0012-7094-61-02828-9 |
| Reference:
|
[2] B. R. Choe: Projections, the weighted Bergman spaces, and the Bloch space.Proc. Am. Math. Soc. 108 (1990), 127–136. Zbl 0684.47022, MR 0991692, 10.1090/S0002-9939-1990-0991692-0 |
| Reference:
|
[3] F. Forelli and W. Rudin: Projections on spaces of holomorphic functions in balls.Indiana Univ. Math. J. 24 (1974), 593–602. MR 0357866 |
| Reference:
|
[4] S. Gadbois: Mixed-norm generalizations of Bergman space and duality.Proc. Am. Math. Soc. 104 (1988), 1171–1180. MR 0948149, 10.1090/S0002-9939-1988-0948149-3 |
| Reference:
|
[5] C. Kolaski: A new look at a theorem of Forelli and Rudin.Indiana Univ. Math. J. 28 (1979), 495–499. Zbl 0412.41023, MR 0529680 |
| Reference:
|
[6] O. Kurens and K. H. Zhu: A class of integral operators on the unit ball of $\mathbb{C}^n$.Integr. Equ. Oper. Theory 56 (2006), 71–82. MR 2256998, 10.1007/s00020-005-1411-3 |
| Reference:
|
[7] Y. M. Liu: Boundedness of the Bergman type operators on mixed norm space.Proc. Am. Math. Soc. 130 (2002), 2363–2367. MR 1897461, 10.1090/S0002-9939-02-06332-3 |
| Reference:
|
[8] G. B. Ren and J. H. Shi: Bergman type operator on mixed norm spaces with applications.Chin. Ann. Math., Ser. B 18 (1997), 265–276. MR 1480002 |
| Reference:
|
[9] G. B. Ren and J. H. Shi: Forelli-Rudin type theorem on pluriharmonic Bergman spaces with small exponent.Sci. China, Ser. A 42 (1999), 1286–1291. MR 1749939, 10.1007/BF02876029 |
| Reference:
|
[10] G. B. Ren and J. H. Shi: Gleason’s problem in weighted Bergman space on egg domains.Sci. China, Ser. A 41 (1998), 225–231. MR 1621125, 10.1007/BF02879040 |
| Reference:
|
[11] A. L. Shields and D. L. Williams: Bounded projections, duality and multipliers in spaces of analytic functions.Trans. Am. Math. Soc. 162 (1971), 287–302. MR 0283559 |
| Reference:
|
[12] K. H. Zhu: The Bergman spaces, the Bloch spaces and Gleason’s problem.Trans. Am. Math. Soc. 309 (1988), 253–268. MR 0931533 |
| Reference:
|
[13] K. H. Zhu: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics 226.Springer-Verlag, New York, 2005. MR 2115155 |
| . |
