Growth properties for modified Poisson integrals in a half space

Asymptotic behavior of fractional Laplacians in the half space

“…Motivated by Zhang and Deng [25] and Mizuta and Shimomura [18] and Theorem 2.1, the aim of this paper is to find the asymptotic behaviors of the Poisson-type integral P a ½f ðxÞ of the fractional Laplacian and the modified fractional Laplacian in a half space of R n .…”

“…The growth properties of analytic functions with order less than 2 in the half plane was studied in [24]. Asymptotic behaviors for different kinds of potentials were also discussed in [1,12,13,16,18].…”

“…In the present article, motivated by those works in [1,18,24,25], we study the asymptotic behaviors of Poisson integral fractional Laplacians in the half space of R n . By the similar methods in studying Poisson integral fractional Laplacians, we estimate the asymptotic behavior of modified Poisson integrals of fractional Laplacians.…”

On Estimates for Maximal Operators Associated with Tangential Regions

“…Di Biase [8], Di Biase-Stokolos-Svensson-Weiss [9]. Sjögren [39,40,41], Rönning [32,33,34], Katkovskaya-Krotov [22,26], Krotov [24,25], Brundin [6], Mizuta-Shimomura [29], Aikawa [3] studied fractional Poisson integrals with respect to the fractional power of the Poisson kernel and obtained some tangential convergence properties for such integrals. More precisely they considered the integrals Theorem C (see [39,32,33]).…”

Growth Estimates and Integral Representations of Harmonic and Subharmonic Functions

“…To obtain a solution of Dirichlet problem for the boundary date f , as in [38], [39], [41] and [31], we use the following modified functions defined by…”