A covering theorem for typically real functions

Typically Real Harmonic Functions

We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.

Typically-real Functions with Assigned Zeros

is said to be typically-real of order p, if in (1.1) the coefficients bn are all real and if either (I) f(z) is regular in |a| =S1 and 3/(ei9) changes sign 2p times as z = eie traverses the boundary of the unit circle, or (II) f(z) is regular in | z\ < 1 and if there is a p < 1 such that for each r in p<r<l, $f(reie) changes sign 2p times as z = reie traverses the circle \z\ =r. This set of fun...

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

A Covering Theorem with Applications

We prove a Covering Theorem that allows us to prove modified norm inequalities for general maximal operators. We will also give applications to convergence of a sequence of linear operators and the differentiation of the integral.

Typically Real Logharmonic Mappings