Integral transforms for logharmonic mappings

Typically Real Logharmonic Mappings

A Note on Logharmonic Mappings

where (a) m is nonnegative integer, (b) β= a(0)(1+a(0))/(1−|a(0)|2) and therefore, β >−1/2, (c) h and g are analytic in U , g(0)= 1, and h(0)≠ 0. Univalent logharmonic mappings on the unit disc have been studied extensively. For details see [1, 2, 3, 4, 5, 6, 7, 8]. Suppose that f is a univalent logharmonic mapping defined on the unit disc U . Then, if f(0) = 0, the function F(ζ) = log(f (eζ)) ...

A Factorization Theorem for Logharmonic Mappings

We give the necessary and sufficient condition on sense-preserving logharmonic mapping in order to be factorized as the composition of analytic function followed by a univalent logharmonic mapping. Let D be a domain of C and denote by H(D) the linear space of all analytic functions defined on D. A logharmonic mapping is a solution of the nonlinear elliptic partial differential equation f z = a ...

Henstock-Kurzweil Integral Transforms

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...

Weighted norm inequalities for integral transforms

Weighted (L, L) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the condit...