Aleksandrov, Anderson and Nicolau have found examples of inner functions that are in the little Bloch space with a specific rate of convergence to zero. As a corollary they obtain positive singular measures defined in the boundary of the unit disc that are simoultaneously symmetric and Kahane. Nevertheless their construction is very indirect. We give an explicit example of such measures by mean...

Let D be a bounded homogeneous domain in C. In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H∞(D) into the Bloch space of D. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit bal...

The spin Hall effect is a phenomenon of inducing spin current by an external electric field. We recently proposed that this effect can occur in p-type semiconductors without relying upon any disorder scattering [S. Murakami et al., Science 301, 1348 (2003)]. This intrinsic effect is due to the “Berry phase in momentum space”, representing topological structure of the Bloch band structure. We ex...

Let H(B) denote the space of all holomorphic functions on the unit ball B Cn. We investigate the following integral operators: Tg( f )(z)= ∫ 1 0 f (tz) g(tz)(dt/t), Lg( f )(z)= ∫ 1 0 f (tz)g(tz)(dt/t), f H(B), z B, where g H(B), and h(z)= ∑n j=1 zj(∂h/∂zj)(z) is the radial derivative of h. The operator Tg can be considered as an extension of the Cesàro operator on the unit disk. The boundedness...

A new interpolation problem is defined for the Bloch space and some partial results are obtained. §

We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...