Acta Mathematica Hungarica

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

On Certain Integral Operators of Fractional Type

  • T. Godoy
  • M. Urciuolo


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 \(\frac{1}{q} = \frac{1}{p} - r\).


Integral Operator Regularity Condition Fractional Type Suitable Regularity Suitable Regularity Condition 
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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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