Let ω be a radial weight on the unit disc of the complex plane D and denote by ω(r) = 1 r ω(s) ds the tail integrals. A radial weight ω belongs to the class D if satisfies the upper doubling condition sup 0<r< ∞. If ν ...

Let ω and ν be radial weights on the unit disc of the complex plane, and denote σ = ωp′ ν− p′ p and ωx = ∫ 1 0 sxω(s) ds for all 1 ≤ x < ∞. Consider the one-weight inequality ‖Pω (f )‖Lp ν ≤ C‖f ‖Lp ν , 1 < p < ∞, ...

For a fixed analytic function $g$ on the unit disc $\D$, we consider the analytic paraproducts induced by $g$, which are defined by $T_gf(z)= \int_0^z f(\z)g'(\z)\,d\z$, $S_gf(z)= \int_0^z f'(\z)g(\z)\,d\z$, and $M_gf(z)= ...

We consider the Hilbert-type operator defined by Hω(f)(z)=∫10f(t)(1z∫z0Bωt(u)du)ω(t)dt, where {Bωζ}ζ∈D are the reproducing kernels of the Bergman space A2ω induced by a radial weight ω in the unit disc D. We prove ...

For analytic functions g on the unit disk with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator Tg( f )(z) = z 0 f (ζ )g(ζ ) dζ from a space X of analytic functions ...

In [1] it is shown that the Bloch space in the unit disc has the following radicality property: if an analytic function g satisfies that , then , for all . Since coincides with the space of analytic symbols g such that the ...