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Boundary values of zero-smooth Besov analytic functions in the unit ball of ${ℂ}^n$ are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.

The mutual singularity problem for measures with restrictions on the spectrum is studied. The $d$-pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.

Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.

Let $\omega :(0,\infty )\to (0,\infty )$ be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure $\mu \in {ℝ}^n$ is called $\omega$-Zygmund if there exists a positive constant $C$ such that $|\mu \left(Q_{+}\right)-\mu \left(Q_{-}\right)|\le C\omega \left(\ell \left(Q_{+}\right)\right)\left|Q_{+}\right|$ for any pair $Q_{+},Q_{-}\subset {ℝ}^n$ of adjacent cubes of the same size. Similarly, $\mu$ is called an $\omega$- symmetric measure if there exists a positive constant $C$ such that $|\mu \left(Q_{+}\right)/\mu \left(Q_{-}\right)-1|\le C\omega \left(\ell \left(Q_{+}\right)\right)$ for any pair $Q_{+},Q_{-}\subset {ℝ}^n$ of adjacent cubes of the same size, $\ell \left(Q_{+}\right)=\ell \left(Q_{-}\right)\<1$. We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...