We give a new proof of Ohta’s Λ-adic Eichler-Shimura isomorphism using p-adic Hodge theory and the results of Bloch-Kato and Hyodo on p-adic étale cohomology.

A description of the closure in the Bloch norm of the Bloch functions that are in a Hardy space is given. The result uses the classical estimates for the Lusin area function. §

New criteria for the boundedness and the compactness of the generalized weighted composition operators from mixed norm spaces into Blochtype spaces are given in this paper.

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uCφ from Bloch type spaces to Zygmund type spaces in D in terms of u,φ, their derivatives and the n-th power φ of φ. Moreover, we obtain some similar estimates for their essential norms. From which...

Kato established higher local reciprocity map (see section 5 and [K1, Th. 2 of §6] (two-dimensional case), [K2, Th. II], [K3, §4]) using in particular this theorem. In this section we deduce the reciprocity map for higher local fields from this theorem and Bloch–Kato’s theorem of section 4. Our approach which uses generalized class formations simplifies Kato’s original argument. We use the nota...

We investigate a system described by two real scalar fields coupled with gravity in (4, 1) dimensions in warped spacetime involving one extra dimension. The results show that the parameter which controls the way the two scalar fields interact induces the appearence of thick brane which engenders internal structure, driving the energy density to localize inside the brane in a very specific way.

We study subharmonic functions in the unit ball of R , with either a Bloch–type growth or a growth described through integral conditions involving some involutions of the ball. Considering mappings u 7→ gu between sets of functions with a prescribed growth, we study how the choice of these sets is related to the growth of the function g.

We study the boundedness and compactness of the differences of two weighted composition operators acting from the Bloch space B to the space H∞ of bounded analytic functions on the open unit disk. Such a study has a relationship to the topological structure problem of composition operators on H∞. Using this relation, we will estimate the operator norms and the essential norms of the differences...

A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms o...