Let B denote the Beurling-Ahlfors transform defined on L(C), 1 < p < ∞. The celebrated conjecture of T. Iwaniec states that its L norm ‖B‖p = p∗ − 1 where p∗ = max{p, p p−1}. In this paper the new upper estimate ‖B‖p ≤ 1.575 (p − 1), 1 < p < ∞ is found.

Density conditions for wavelet systems with arbitrary sampling points to be frames are studied. We show that for a wavelet system generated by admissible functions and irregular affine lattices to be a frame, the sampling points must have a positive lower Beurling density. The same is true for wavelet systems with arbitrary sampling points and nice generating functions.

In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

In this paper, we consider several questions emerging from the Beurling-Lax-Halmos Theorem, which characterizes shift-invariant subspaces of vector-valued Hardy spaces. The Theorem states that a backward subspace is model space $\mathcal{H}(\Delta) \equiv H_E^2 \ominus \Delta H_{E}^2$, for some inner function $\Delta$. Our first question calls description set $F$ in $H_E^2$ such $\mathcal{H}(\D...

Cotangent sums play a significant role in the Nyman-Beurling criterion for Riemann Hypothesis. Here we investigate maximum of values these cotangent over various sets rational numbers short intervals.

Some aspects of the theory of Boolean algebras and distributive lattices -in particular, the Stone Representation Theorems and the properties of filters and ideals -are analyzed in a constructive setting.