Embedding Bergman spaces into tent spaces

作者：Angel Pelaez Jose; Rattya Jouni; Sierra Kian

来源：Mathematische Zeitschrift, 2015, 281(3-4): 1215-1237.

DOI：10.1007/s00209-015-1528-2

• Tent space
• Carleson measure
• Area operator
• Integral operator
• Bergman space
• Hardy space

Let A(omega)(p) denote the Bergman space in the unit disc D of the complex plane induced by a radial weight. with the doubling property integral(1)(r) omega(s) ds <= C integral(1)(1+r/2) omega(s) ds. The tent space T-s(q) (nu, omega) consists of functions such that
parallel to f parallel to(q)(Tqs(nu,omega)) = integral(D) integral(Gamma(zeta)) vertical bar f(z)vertical bar(s) d nu (z))(q/s) omega(zeta) dA(zeta) < infinity, 0 < q, s < infinity.
Here Gamma(zeta) is a non-tangential approach region with vertex zeta in the punctured unit disc D\{0}. We characterize the positive Borel measures nu such that A(omega)(p) is embedded into the tent space T-s(q) (nu,omega), where 1+ s/p - s/q > 0, by considering a generalized area operator. The results are provided in terms of Carleson measures for A(omega)(p).

• 出版日期2015-12