A Characterization of Certain Types of Hankel Symbols on the Drury–Arveson Space
Tóm tắt
For a class of symbols
$$\varphi \in H^2_{d + 1}$$
, a characterization of those particular
$$\varphi $$
which induce a bounded Hankel operator on the Drury–Arveson Space is given in terms of a Carleson measure condition on the function
$$\varphi $$
.
Tài liệu tham khảo
Arcozzi, N., Rochberg, R., Sawyer, E.: Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls. Adv. Math. 218(4), 1107–1180 (2008)
Arcozzi, N., Rochberg, R., Sawyer, E., Wick, B.D.: Bilinear forms on the Dirichlet space. Anal. PDE 3(1), 21–47 (2010)
Cascante, C., Fàbrega, J., Ortega, J.M.: On weighted Toeplitz, big Hankel operators and Carleson measures. Integral Equ. Oper. Theory 66(4), 495–528 (2010)
Cascante, C., Ortega, J.M.: On a characterization of bilinear forms on the Dirichlet space. Proc. Am. Math. Soc. 140(7), 2429–2440 (2012)
Coifman, R.R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. Math. (2) 103(3), 611–635 (1976)
Fang, Q., Xia, J.: Commutators and localization on the Drury-Arveson space. J. Funct. Anal. 260(3), 639–673 (2011)
Jevtić, M.: On the Carleson measure characterization of BMOA functions on the unit ball. Proc. Am. Math. Soc. 114(2), 379–386 (1992)
Richter, S., Sundberg, C.: Weak products of Dirichlet functions. J. Funct. Anal. 266(8), 5270–5299 (2014)
Richter, S., Sunkes, J.: Hankel operators, invariant subspaces, and cyclic vectors in the drury-arveson space. Proc. Am. Math. Soc. 144(2016), 2575–2586 (2016)
Rochberg, R., Wu, Z.J.: A new characterization of Dirichlet type spaces and applications. Ill. J. Math. 37(1), 101–122 (1993)
Shalit, O.: Operator theory and function theory in Drury-Arveson space and its quotients (2014, Preprint)
Zhu, K.H.: Hankel operators on the Bergman space of bounded symmetric domains. Trans. Am. Math. Soc. 324(2), 707–730 (1991)
Zhu, K.: Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226. Springer-Verlag, New York (2005)