On lpl^p -multipliers of functions analytic in the disk

We consider bounded analytic functions in domains generated by sets that have Littlewood--Paley property. We show that each such function is an $l^p$ -multiplier.Comment: 6 pages, minor modification on page 2 is made to improve clarit

Thickness conditions and Littlewood--Paley sets

We consider sets in the real line that have Littlewood--Paley properties $\mathrm{LP}(p)$ or $\mathrm{LP}$ and study the following question: How thick can these sets be?Comment: 15 pages, v2 has minor modifications to improve clarity, typos remove

Absolutely convergent Fourier series. An improvement of the Beurling--Helson theorem

We consider the space $A(\mathbb T)$ of all continuous functions $f$ on the circle $\mathbb T$ such that the sequence of Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z\}$ belongs to $l^1(\mathbb Z)$. The norm on $A(\mathbb T)$ is defined by $\|f\|_{A(\mathbb T)}=\|\hat{f}\|_{l^1(\mathbb Z)}$. According to the known Beurling--Helson theorem, if $\phi : \mathbb T\rightarrow\mathbb T$ is a continuous mapping such that $\|e^{in\phi}\|_{A(\mathbb T)}=O(1), ~n\in\mathbb Z,$ then $\phi$ is linear. It was conjectured by Kahane that the same conclusion about $\phi$ is true under the assumption that $\|e^{in\phi}\|_{A(\mathbb T)}=o(\log |n|)$. We show that if $\|e^{in\phi}\|_{A(\mathbb T)}=o((\log\log |n|/\log\log\log |n|)^{1/12})$ then $\phi$ is linear.Comment: A typo on page 14 line 4 is corrected. A typo on page 16 line 5 is corrected. Notation in the proof of Lemma 2 are replaced with more readable one

B Decays as a Probe of Spontaneous CP-Violation in SUSY Models

We consider phenomenological implications of susy models with spontaneously broken CP-symmetry. In particular, we analyze CP-asymmetries in B decays and find that the predictions of these models are vastly different from those of the SM. These features are common to NMSSM-like models with an arbitrary number of sterile superfields and the MSSM with broken R-parity.Comment: Talk given at SUSY'99, 14-19 June, Fermilab, Batavia, I