대한수학회지 (Journal of the Korean Mathematical Society)

  • 제40권6호
  • /
  • Pages.999-1014
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  • 2003
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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BOUNDEDNESS AND INVERSION PROPERTIES OF CERTAIN CONVOLUTION TRANSFORMS

  • Yakubovich, Semyon-B. (Department of Pure Mathematics Faculty of Sciences University of Porto)
  • 발행 : 2003.11.01
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초록

For a fixed function h we deal with a class of convolution transforms $f\;{\rightarrow}\;f\;*\;h$, where $(f\;*\;h)(x)\;=\frac{1}{2x}\;{\int_{{R_{+}}^2}}^{e^1{\frac{1}{2}}(x\frac{u^2+y^2}{uy}+\frac{yu}{x})}\;f(u)h(y)dudy,\;x\;\in\;R_{+}$ as integral operators $L_p(R_{+};xdx)\;\rightarrow\;L_r(R_{+};xdx),\;p,\;r\;{\geq}\;1$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $L_2(R_{+};xdx)$ are obtained.

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참고문헌

  1. Higher Transcendental Functions v.Ⅱ A.Erdelyi;W.Magnus;F.Oberhettinger;F.G.Tricomi
  2. Fourier Series. A Modern Introduction v.Ⅱ R.E.Edwards
  3. Dokl. AN SSR v.68 no.4 Analog of the Parseval theorem for the one integral transform N.N.Lebedev
  4. Gordon and Breach v.Ⅰ;Ⅱ Integrals and Series;Elementary Functions;Special Functions A.P.Prudnikov;Yu.A.Brychkov;O.I.Marichev
  5. The Use of Integral Transforms I.N.Sneddon
  6. Index Transforms S.B.Yakubovich

피인용 문헌

  1. Boundedness in weighted Lp spaces for the Kontorovich–Lebedev–Fourier generalized convolutions and applications vol.28, pp.8, 2017, https://doi.org/10.1080/10652469.2017.1330825
  2. The convolution for the Kontorovich–Lebedev transform revisited vol.440, pp.1, 2016, https://doi.org/10.1016/j.jmaa.2016.03.052
  3. On Fourier – Kontorovich–Lebedev generalized convolution transforms vol.28, pp.4, 2017, https://doi.org/10.1080/10652469.2017.1281922
  4. On a progress in the Kontorovich–Lebedev transform theory and related integral operators vol.19, pp.7, 2008, https://doi.org/10.1080/10652460801936663
  5. On the least values of Lp-norms for the Kontorovich–Lebedev transform and its convolution vol.131, pp.2, 2004, https://doi.org/10.1016/j.jat.2004.10.007