The Schatten norm for the nuclear operator B*?B? was estimated from both sides. Here B? : L2 ? is Berezin transform regarding Fock spaces in plane. Also, we found case of unweighted Lebesgue spaces.

We prove that non-commutative martingale transforms are of weak type (1, 1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1 is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x = (xn) ∞ n=1 in L 1(M), adapted to (Mn)n=1, and any sequence of signs (εn) ∞ n=1, ∥∥∥∥ε1x1 + N ∑ n=2 εn(xn...

Namita Das P. G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, Orissa 751004, India Correspondence should be addressed to Namita Das, [email protected] Received 23 July 2009; Revised 7 September 2009; Accepted 14 October 2009 Recommended by Palle Jorgensen We have shown that if the Toeplitz operator Tφ on the Bergman space La D belongs to the Schatten class Sp, 1 ≤...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...