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Acta Mathematica Hungarica

, Volume 82, Issue 1–2, pp 99–105 | Cite as

On Certain Integral Operators of Fractional Type

  • T. Godoy
  • M. Urciuolo
Article

Abstract

In this paper we study integral operators of the form
$$T\,f\left( x \right) = \int {k_1 \left( {x - a_1 y} \right)k_2 \left( {x - a_2 y} \right)...k_m \left( {x - a_m y} \right)f\left( y \right)dy} ,$$
$$k_i \left( y \right) = \sum\limits_{j \in Z} {2^{\frac{{jn}}{{q_i }}} } \varphi _{i,j} \left( {2^j y} \right),\,1 \leqq q_i < \infty ,\frac{1}{{q_1 }} + \frac{1}{{q_2 }} + ... + \frac{1}{{q_m }} = 1 - r,$$
\(0 \leqq r < 1\), and \(\varphi _{i,j}\) satisfying suitable regularity conditions. We obtain the boundedness of \(T:L^p \left( {R^n } \right) \to T:L^q \left( {R^n } \right)\) for \(1 < p < \frac{1}{r}\) and \(\frac{1}{q} = \frac{1}{p} - r\).

Keywords

Integral Operator Regularity Condition Fractional Type Suitable Regularity Suitable Regularity Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    T. Godoy, and M. Urciuolo, About the L p boundedness of some integral operators, Revista de la UMA, 38 (1993), 192–195.Google Scholar
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    T. Godoy and M. Urciuolo, About the L p boundedness of integral operators with kernels of the form k 1(x \t-y)k 2(x + y), Math. Scand., 78 (1996), 84–92.Google Scholar
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    F. Ricci and E. Stein, Harmonic analysis on nilpotent groups and singular integrals. III, Fractional integration along manifolds, J. Funct. Anal., 86 (1989), 360–389.Google Scholar
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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • T. Godoy
    • 1
  • M. Urciuolo
    • 1
  1. 1.Facultad de MatemáticaAstronomía y Física Ciudad UniversitariaCórdobaArgentina

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