arXiv subjects
Publications and source records attributed to Martin At. Stanev.
In the present work weighted area integral means $M_{p,φ}(f;{\mathrm {Im}}z)$ are studied and it is proved that the function $y\to \log M_{p,φ}(f;y)$ is convex in the case when $f$ belongs to a Hardy space on the upper half-plane.
Some theorems on convex functions are proved and an application of these theorems in the theory of weighted Banach spaces of holomorphic functions is investigated, too. We prove that $H_v(G)$ and $H_{v_0}(G)$ are exactly the same spaces as $H_w(G)$ and $H_{w_0}(G)$ where $w$ is the smallest log-concave majorant of $v$. This investigation is based on the theory of convex functions and some specific properties of the weighted banach spaces of holomorphic functions under considaration and we do not use the theory of associated weights.
The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In this paper, we present some new results, too, and results that extend some of our PhD(1993year) disertation theorems. We hope this letter will be useful for obtaining some email friendships.