On representation of functions that satisfy Lipschitz condition as convolution of functions from Lorentz spaces

B.I. Peleshenko

doi:10.15421/241016

On representation of functions that satisfy Lipschitz condition as convolution of functions from Lorentz spaces

B.I. Peleshenko (Dnipropetrovsk State Agrarian and Economic University)

Abstract

Any $$$2\pi$$$-periodic function from the Lipschitz space $$$\Lambda_b^{\alpha}$$$ can be represented by way of the convolution of the functions from the Lorentz spaces $$$L_{p,r}$$$ and $$$L_{b,r'}$$$ in the case when $$$1 \leqslant b < \infty$$$, $$$0 < 1 - p^{-1} < \alpha < 1$$$ and the numbers $$$r$$$, $$$r'$$$ are picked in the corresponding way.

Keywords

convolution of the functions; Lipschitz space

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References

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