In order to get estimates on the solutions of the equation ∂̄u = ω on Stein manifold, we introduce a new method the ”raising steps method”, to get global results from local ones. In particular it allows us to transfer results form open sets in C to open sets in a Stein manifold. Using it we get L − L results for solutions of equation ∂̄u = ω with a gain, s > r, in strictly pseudo convex domains i...

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If A is a reflexive, amenable Banach algebra such that for each maximal left ideal L of A (i) the quotient A/L has t...

We consider the L-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigenspectra of the unfused transfer matrix is obtained from the functional relations u...

The vulnerability of water bodies to contamination within the neighbourhood of open mine cast environ cannot be overemphasized. Evidence of radioactive trace elements associated with the target minerals in the Plateau State (Nigeria) showed the extent of this vulnerability. In order to address this challenge, the radioactivity levels of water samples from mine ponds, streams, wells, and borehol...

In this paper, we study the L boundedness of a class of parametric Marcinkiewicz integral operators with rough kernels in L(log L)(Sn−1). Our result in this paper solves an open problem left by the authors of ([6]).

Abstract Let $$\mathcal {B}$$ B be a homogeneous differential operator of order $$l=1$$ l = 1 or $$l=2$$ 2 . We show that sequence functions the form $$(\mathcal {B}u_j)_j$$ ( u</mml:...