Lp Regularity of some weighted Bergman projections on the unit disc

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

We show that weighted Bergman projections, corresponding to weights of the form M(z)(1-|z|2)\alpha, where a > -1 and M(z) is a radially symmetric, strictly positive and at least C2 function on \overline{D}, are Lp regular.

Anahtar Kelimeler:

Weighted Bergman projection, Coefficient multipliers

Lp Regularity of some weighted Bergman projections on the unit disc

Keywords:

Weighted Bergman projection, Coefficient multipliers,

PDF

___

Since Lemma 3.2 is established, we conclude the proof of Theorem 1.2. Buckley, S. M. and Koskela, P. and Vukoti´c, D.: Fractional integration, diﬀerentiation, and weighted Bergman spaces. Math. Proc. Cambridge Philos. Soc. 2, 369–385 (1999).
Duren, P. and Schuster, A.: Bergman spaces. Providence, RI. American Mathematical Society 2004.
Forelli, F. and Rudin, W.: Projections on spaces of holomorphic functions in balls. Indiana Univ. Math. J. 24, –602 (1974/75).
Hedenmalm, H. and Korenblum, B. and Zhu, K.: Theory of Bergman spaces. New York. Springer-Verlag 2000.
Zhu, K. H.: Duality of Bloch spaces and norm convergence of Taylor series. Michigan Math. J. 38, 89–101 (1991)
Zhu, K.: Operator theory in function spaces. Providence, RI. American Mathematical Society 2007. Yunus E. ZEYTUNCU
Department of Mathematics, Texas A&M University, College Station, Texas 77843, USA e-mail: zeytuncu@math.tamu.edu