Abstract We establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) x with doubling property $$\omega (0,2t)\le C\omega (0,t)$$ <mm...

An increasing homeomorphism \(h\) on the real line \(\mathbb{R}\) is said to be strongly symmetric if it can extended a quasiconformal of upper half plane \(\mathbb{U}\) onto itself whose Beltrami coefficient \(\mu\) induces vanishing Carleson measure \(|\mu(z)|^2/y\,dx\,dy\) \(\mathbb{U}\). We will deal with class homeomorphisms and its Teichmüller space, which we call VMO-Teichmüller space. I...

By a standard approximation argument it follows that S[f ] may be meaningfully defined as a continuous function in ξ for almost every x whenever f ∈ L and the a priori bound of the theorem continues to hold for such functions. Theorem 1.1 is intimately related to almost everywhere convergence of partial Fourier sums for functions in L[0, 1]. Via a transference principle [12], it is indeed equiv...

For a collection E of dyadic intervals, a Banach space X, and p ∈ (1, 2] we assume the upper lp estimates