Let ${\bold D}$ denote the unit disk in the complex plane and let $m$ be the area Lebesgue measure on ${\bold D}$. Given a positive integrable function $w$ (a weight) on ${\bold D}$, let $L^p_{\rm… Expand

A celebrated theorem in operator theory is A. Beurling's description of the invariant subspaces in $H^2$ in terms of inner functions [Acta Math. {\bf81} (1949), 239--255; MR0027954 (10,381e)]. To do… Expand

Using harmonic maps we provide an approach towards obtaining explicit solutions to the incompressible two-dimensional Euler equations. More precisely, the problem of finding all solutions which in… Expand

Let g be an analytic function on the unit disk D . We study the operator on the Hardy spaces Hp . We show that Tg is bounded on Hp , 1 ≤ p < ∞ it and only if g ∊ BMOA and compact if and only if g ∊… Expand

Let $w$ be a positive on $[0,1)$ which is concave, decreasing and tends to $0$ at $1$. The space $H_w$ of analytic functions $f$ satisfying $\|f\|^2_w\coloneq… Expand

Let C∞(a,b) be the Fréchet space of all complex-valued infinitely differentiable functions on a (finite or infinite) interval (a, b) ⊂ ℝ. Let L ⊂ C∞(a,b) be a closed subspace such that DL ⊂ L, where… Expand

Let μ be a finite positive measure on the closed disk D in the complex plane, let 1 ≤ t < ∞, and let P t(μ) denote the closure of the analytic polynomials in Lt(μ). We suppose that D is the set of… Expand