**
Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 131-140 (2004)
**

#
Translation Invariant Operators on Hardy Spaces over Vilenkin Groups

##
J.E. Daly and S Fridli

University of Colorado, Eötvös L. University

**Abstract:**
We show that a number of well known multiplier theorems for Hardy spaces over Vilenkin groups follow immediately from a general condition on the kernel of the multiplier operator. In the compact case, this result shows that the multiplier theorems of Kitada, Tateoka, Daly-Phillips, and Simon are best viewed as providing conditions on the partial sums of the Fourier-Vilenkin series of the kernel rather than explicit conditions on the Fourier-Vilenkin coefficients themselves. The theorem is used to prove an extension of the Marcinkiewicz multiplier theorem for Hardy spaces.

**Keywords:** Convolution operators, Hardy spaces, Vilenkin groups, multipliers.

**Classification (MSC2000):** 42A45

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2004 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
for the EMIS Electronic Edition
*