For 0 < p ≤ ∞ and 0 < q ≤ ∞, the space of Hardy-Bloch type B(p, q) consists of those functions f which are analytic in the unit disk D such that (1− r)Mp(r, f ′) ∈ Lq(dr/(1− r)). We note that B(∞,∞)… (More)

Let f be a harmonic homeomorphism of the unit disk onto itself. The following conditions are equivalent: (a) f is quasiconformal; (b) f is bi-Lipschitz in the Euclidean metric; (c) the boundary… (More)

Let 2 ≤ p < ∞ and let X be a complex Banach space. It is shown that X is p-uniformly PL-convex if and only if there exists λ > 0 such that ‖f‖Hp(X) ≥ ( ‖f(0)‖p + λ ∫ D (1− |z|2)p−1‖f ′(z)‖pdA(z) )1/p… (More)

We consider the space B logα , of analytic functions on the unit disk D, defined by the requirement ∫ D |f (z)|φ(|z|) dA(z) < ∞, where φ(r) = log(1/(1 − r)) and show that it is a predual of the… (More)

The inequalities of Hardy–Littlewood type play very important role in many theorems concerning convergence or summability of orthogonal series. In the applications many times their converses are also… (More)

It is proved that an orientation-preserving homeomorphism ψ of the real axis can be extended to a quasiconformal harmonic homeomorphism of the upper half-plane if and only if ψ is bi-Lipschitz and… (More)

The solid hulls of the Hardy–Lorentz spaces Hp,q , 0 < p < 1, 0 < q 6∞ and Hp,∞ 0 , 0 < p < 1, as well as of the mixed norm space H p,∞,α 0 , 0 < p 6 1, 0 < α <∞, are determined. Introduction In… (More)

We define and characterize the harmonic Besov space Bp, 1 ≤ p ≤ ∞, on the unit ball B in Rn. We prove that the Besov spaces Bp, 1 ≤ p ≤ ∞, are natural quotient spaces of certain Lp spaces. The dual… (More)

This is a collection of some known and some new facts on the holomorphic and the harmonic version of the Hardy-Stein identity as well as on their extensions to the real and the complex ball. For… (More)

We consider the action of the operator ℒg(z) = (1 - z)(-1)∫ z (1)f(ζ)dζ on a class of "mixed norm" spaces of analytic functions on the unit disk, X = H α,ν (p,q) , defined by the requirement g ∈ X ⇔… (More)