BOUNDEDNESS AND INVERSION PROPERTIES OF CERTAIN CONVOLUTION TRANSFORMS

Title & Authors
BOUNDEDNESS AND INVERSION PROPERTIES OF CERTAIN CONVOLUTION TRANSFORMS
Yakubovich, Semyon-B.;

Abstract
For a fixed function h we deal with a class of convolution transforms $\small{f\;{\rightarrow}\;f\;*\;h}$, where $\small{(f\;*\;h)(x)\;=\frac{1}{2x}\;{\int_{{R_{+}}^2}}^{e^1{\frac{1}{2}}(x\frac{u^2+y^2}{uy}+\frac{yu}{x})}\;f(u)h(y)dudy,\;x\;\in\;R_{+}}$ as integral operators $\small{L_p(R_{+};xdx)\;\rightarrow\;L_r(R_{+};xdx),\;p,\;r\;{\geq}\;1}$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $\small{L_2(R_{+};xdx)}$ are obtained.
Keywords
convolution transform;Kontorovich-Lebedev transform;Young inequality;
Language
English
Cited by
1.
On the least values of Lp-norms for the Kontorovich–Lebedev transform and its convolution, Journal of Approximation Theory, 2004, 131, 2, 231
2.
On a progress in the Kontorovich–Lebedev transform theory and related integral operators, Integral Transforms and Special Functions, 2008, 19, 7, 509
3.
The convolution for the Kontorovich–Lebedev transform revisited, Journal of Mathematical Analysis and Applications, 2016, 440, 1, 369
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