The existence of a weighted mean for almost periodic functions |
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Authors: | Toka Diagana |
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Institution: | Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, DC 20059, USA |
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Abstract: | In a recent paper by Liang et al. (2010) 1], the original question which is that of the existence of a weighted mean for almost periodic functions was raised. In particular, they showed through an example that there exist weights for which a weighted mean for almost periodic functions may or may not exist. In this note we give some sufficient conditions which do guarantee the existence of a weighted mean for almost periodic functions, which will then coincide with the classical Bohr mean. Moreover, we will show that under those conditions, the corresponding weighted Bohr transform exists. |
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Keywords: | 34K14 35B15 42B05 |
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