Related papers: On critical points of Blaschke products
In this paper we provide in $\bFp$ expanding lower bounds for two variables functions $f(x,y)$ in connection with the product set or the sumset. The sum-product problem has been hugely studied in the recent past. A typical result in…
In this paper, the main aim is to discuss the existence of the extreme points and support points of families of harmonic Bloch mappings and little harmonic Bloch mappings. First, in terms of the Bloch unit-valued set, we prove a necessary…
We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic…
We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the…
Consider a finite Blaschke product $f$ with $f(0) = 0$ which is not a rotation and denote by $f^n$ its $n$-th iterate. Given a sequence $\{a_n\}$ of complex numbers, consider the series $F(z) = \sum_n a_n f^n(z).$ We show that for any $w…
In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the…
In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs…
The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz…
We present a characterization of one-component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by J. Cima and R. Mortini. In particular we prove…
A description of the Bloch functions that can be approximated in the Bloch norm by functions in the Hardy space $H^p$ of the unit ball of $\Cn$ for $0<p<\infty$ is given. When $0<p\leq1$, the result is new even in the case of the unit disk.
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…
The Blaschke-Santal\'o Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and only by) ellipsoids. In this paper we give a Fourier analytic proof of this fact.
Let $X$ be a compact subset of the complex plane and $x \in X$. A necessary and sufficient condition is given in terms of Hausdorff contents for the existence of a bounded point derivation at $x$ on the space of vanishing Campanato…
For $0<s<1$, let $\{z_n\}$ be a sequence in the open unit disk such that $\sum_n (1-|z_n|^2)^s \delta_{z_n}$ is an $s$-Carleson measure. In this paper, we consider the connections between this $s$-Carleson measure and the theory of M\"obius…
We show that in a scale of weighted Dirichlet spaces $D_{\alpha}$, including the Bergman space, given any finite Blaschke product $B$ there exists an equivalent norm in $D_{\alpha}$ such that $B$ satisfies the wandering subspace property…
In this paper we first consider another version of the Rogosinski inequality for analytic functions $f(z)=\sum_{n=0}^\infty a_nz^n$ in the unit disk $|z| < 1$, in which we replace the coefficients $a_n$ $(n= 0,1,\ldots ,N)$ of the power…
In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convolution formula and combing special GCD sums, our result…
In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the…
It is well known that the bounding curve of the central hyperbolic component of the Multibrot set in the parameter space of unicritical degree $d$ polynomials is an epicycloid with $d-1$ cusps. The interior of the epicycloid gives the…
Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy…