Geodesic
On the uniform boundedness of the family of shifts of Steklov functions in weighted Lebesgue spaces with variable exponent
Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 93-99

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The problem of the uniform boundedness of the Steklov functions shifts families of the form $ S_{\lambda,\tau}(f)=S_{\lambda}(f)(x+\tau)=\lambda\int_{x+\tau-\frac 1{2\lambda}}^{x+\tau+\frac 1{2\lambda}}f(t)dt $ was considered. It was shown that these shifts are uniformly bounded in weighted variable exponent Lebesgue spaces $L^{p(x)}_{2\pi,w}$, where $w=w(x)$ is the weight function satisfying the analogue of Muckenhoupt's condition.
Keywords: Lebesgue spaces with variable exponent, Dini – Lipschitz condition, Steklov operators. 
@article{DEMR_2017_8_a8,
     author = {T. N. Shakh-Emirov},
     title = {On the uniform boundedness of the family of shifts of {Steklov} functions in weighted {Lebesgue} spaces with variable exponent},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {93--99},
     publisher = {mathdoc},
     volume = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2017_8_a8/}
}
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T. N. Shakh-Emirov. On the uniform boundedness of the family of shifts of Steklov functions in weighted Lebesgue spaces with variable exponent. Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 93-99. http://geodesic.mathdoc.fr/item/DEMR_2017_8_a8/