Cancel·lacio i automillora

Aquest article presenta dos problemes d'anàlisi clàssica: el creixement dels quocients incrementals de les funcions de Weierstrass i la regularitat de les mesures de Besicovitch. Aquests problemes s'estudien utilitzant tècniques de martingales diàdiques i s'obtenen diverses versions de la llei del logaritme iterat

Finitely generated ideals in the Nevanlinna class.

In this paper we investigate finitely generated ideals in the Nevanlinna class. We prove analogues to some known results for the algebra of bounded analytic functions $H^{\infty}$. We also show that, in contrast to the $H^{\infty}$ case, the stable rank of the Nevanlinna class is strictly bigger than 1

Traces of the Nevanlinna class on discrete sequences

We show that a discrete sequence $\Lambda$ of the unit disk is the union of $n$ interpolating sequences for the Nevanlinna class $\mathcal{N}$ if and only if the trace of $\mathcal{N}$ on $\Lambda$ coincides with the space of functions on $\Lambda$ for which the divided differences of order $n-1$ are uniformly controlled by a positive harmonic function

The Corona Property in Nevanlinna quotient algebras and interpolating sequences

Let $I$ be an inner function in the unit disk $\mathbb{D}$ and let $\mathcal{N}$ denote the Nevanlinna class. We prove that under natural assumptions, Bezout equations in the quotient algebra $\mathcal{N} / I \mathcal{N}$ can be solved if and only if the zeros of $I$ form a finite union of Nevanlinna interpolating sequences. This is in contrast with the situation in the algebra of bounded analytic functions, where being a finite union of interpolating sequences is a sufficient but not necessary condition. An analogous result in the Smirnov class is proved as well as several equivalent descriptions of Blaschke products whose zeros form a finite union of interpolating sequences in the Nevanlinna class

Distributional inequalities for non harmonic functions

The relationship between the non-tangential maximal function and convenient versions of the area function of a general (non harmonic) function in a upper-half space are studied

Cancel·lacio i automillora

Aquest article presenta dos problemes d'anàlisi clàssica: el creixement dels quocients incrementals de les funcions de Weierstrass i la regularitat de les mesures de Besicovitch. Aquests problemes s'estudien utilitzant tècniques de martingales diàdiques i s'obtenen diverses versions de la llei del logaritme iterat