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A Remark on Certain Integral Operators of Fractional Type

  • Pablo Alejandro Rocha (a1)
Abstract

For m, n ∈ , 1 < m ≤ n, we write n = n1 + … + nm where {n1 , … , nm} ⊂ . Let A1 , . . . , Am be n × n singular real matrices such that

where = {x : Ajx = 0}, dim() = n – nj, and A1 + … + Am is invertible. In this paper we study integral operators of the form

n1 + … + nm = n, , 0 < r < 1, and the matrices Ai’s are as above. We obtain the Hp() − Lq() boundedness of Tr for 0 < p < and .

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References
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[2] Godoy, T. and Urciuolo, M., On certain integral Operators of fractional type. Acta Math. Hungar. 82 (1999), 99105. http://dx.doi.Org/10.1023/A:1026437621978
[3] Krantz, S., Fractional 'Integration on Hardy Spaces. Studia Math. 73 (1982), no. 2, 8794.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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