Notes on zygmund functions
In this paper we study a class of continuous functions satisfying a certain Zyg-mund condition dependent on a parameter γ > 0. It shown that the modulus of continuity of such functions is O(δ(log 1/δ)1-γ) if ∈ (0, 1) and O(δ(log log 1/δ )) if γ = 1. Moreover, these functions are differentiable if...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Academic Publications, Ltd.
2017
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| Subjects: | |
| Online Access: | http://repo.uum.edu.my/21982/1/IJPAM%20112%203%202017%20461%20488.pdf http://repo.uum.edu.my/21982/ http://doi.org/10.12732/ijpam.v112i3.3 |
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| Summary: | In this paper we study a class of continuous functions satisfying a certain Zyg-mund condition dependent on a parameter γ > 0. It shown that the modulus of continuity of such functions is O(δ(log 1/δ)1-γ) if ∈ (0, 1) and O(δ(log log 1/δ )) if γ = 1. Moreover, these functions are differentiable if γ > 1. These results extend the results in literatures [4], [5]. |
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