Estimates of L^p-continuity modulus of ΛBV functions and applications in Fourier series

Abstract

In this article, some estimates of the L ^p modulus of continuity for functions of Λ-bounded variation (ΛBV) are obtained, and as application, the absolute summability of the Fourier series of functions in ΛBV is proved. Especially, it is shown that the Fourier series of functions in {n ^β}BV for 0 < β < 1 is |C, δ| summable when .

Keywords:

• Fourier series
• absolute summability
• Λ-bounded variation
• modulus of continuity

AMS Subject Classifications:

• 42A24
• 26A45

Acknowledgements

This work has been supported by the National Natural Science Foundation of China (No. 10971141, 10871132), the Beijing Natural Science Foundation (No.1092004, 1102011) and the Project of Beijing Education Ministry.