p-adic域,p-级数域的整环子群上微积分算子的Hardy空间有界性

Boundedness of the Calculus Operators on Hardy Spaces Over the Subgroup of Integers of a p adic or p series Field

Ｆ．Ｓｃｈｉｐｐ和Ｗ．Ｒ．Ｗａｄｅ在［１］中证明了单位方体上Ｄｙａｄｉｃ二元微积分算子的混合Ｈａｒｄｙ空间Ｈ＃（Ｉ×Ｉ）的弱型．本文证明了ｐａｄｉｃ域，ｐ级数域的整环子群上一元和二元积分算子与微积分算子的Ｈｒ（Ｇ）与Ｈ＃（Ｇ×Ｇ）（０＜ｒ１）有界性．

F. Schipp and W.R. Wade proved that thetwo-dimensional dyadic calculus operator is of weak-type(1 1)with respect to the hybrid Hardy space H #(I×I). In this paper, we obtained the results that the one-dimensional and two-dimensional calculus operators are respectively bounded on Hardy space H r(G) and hybrid Hardy space H #(G×G) over the subgroup of integers of ap adic or p series field.