IJPAM: Volume 59, No. 3 (2010)

A REMARK ON THE LIMITS OF NONTANGENTIAL
TYPE FOR GENERALIZED POISSON INTEGRALS

Hayato Nakagawa
Graduate School of Mathematics
Nagoya University
Furo-cho, Chikusa-ku, Nagoya, 464-8602, JAPAN
e-mail: m04026b@math.nagoya-u.ac.jp


Abstract.Given an $L^{p}$-function $f$ defined on the boundary of the upper-half space $\mathbb{R}^{n+1}_{+}$, and the fundamental solution $W^{(\alpha)}$ of the parabolic operator of order $\alpha$ on $\mathbb{R}^{n+1}_{+}$, we discuss the boundary behavior of the convolution of $f$ and $W^{(\alpha)}$. Our result generalizes a result of Shapiro [#!shap2!#].

Received: January 28, 2010

AMS Subject Classification: 26A33, 31B25, 35J05

Key Words and Phrases: operators for integration, differentiation of fractional order, boundary behavior, heat equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 3