Fourier Transform and Convolutions on L (p) of a Vector Measure on a Compact Hausdorff Abelian Group

作者：Calabuig J M^*; Galaz Fontes F; Navarrete E M; Sanchez Perez E A

来源：Journal of Fourier Analysis and Applications, 2013, 19(2): 312-332.

DOI：10.1007/s00041-012-9252-3

• Countably additive vector measure
• Space of p-integrable functions
• Fourier transform
• Convolution
• Pettis integrability

Let nu be a countably additive vector measure defined on the Borel subsets of a compact Hausdorff abelian group G. In this paper we define and study a vector valued Fourier transform and a vector valued convolution for functions which are (weakly) integrable with respect to nu. A form of the Riemann Lebesgue Lemma and a Uniqueness Theorem are established in this context. In order to study the vector valued convolution we discuss the invariance under reflection in G of these spaces of integrable functions. Finally we present a Young%26apos;s type inequality in this setting and several relevant examples, namely related with the vector measure associated to different important classical operators coming from Harmonic Analysis.

• 出版日期2013-4