Geodesic
On the norms of generalized translation operators generated by Dunkl-type operators
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 5-31
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The paper establishes the integral representation and improves the norm estimate for the generalized translation operators generated by Dunkl-type operators $$ \Lambda f(x)=f'(x)+\frac{A'(x)}{A(x)}\,\frac{f(x)-f(-x)}2 $$ in the spaces $L_p(\mathbb R)$ with weight $A$. Under some natural conditions on the function $A$, it is proved that these norms do not exceed two. 
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     title = {On the norms of generalized translation operators generated by {Dunkl-type} operators},
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O. L. Vinogradov. On the norms of generalized translation operators generated by Dunkl-type operators. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 5-31. http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a0/

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