IJPAM: Volume 59, No. 3 (2010)
A REMARK ON THE LIMITS OF NONTANGENTIAL
TYPE FOR GENERALIZED POISSON INTEGRALS
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
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 -function
defined on the boundary of the upper-half space
, and the fundamental solution
of the parabolic operator of order
on
, we discuss the boundary behavior of the convolution of
and
. 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