Conjugate functions on spaces of parabolic Bloch type

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Abstract

Let <i>H</i> be the upper half-space of the (<i>n</i>+1)-dimensional Euclidean space. Let 0 < α ≤ 1 and <i>m</i>(α) = min {1, 1/(2α)}. For σ > −<i>m</i>(α), the α-parabolic Bloch type space ${\cal B}$<sub>α</sub>(σ) on <i>H</i> is the set of all solutions <i>u</i> of the equation (∂/∂<i>t</i> + (−Δ<sub><i>x</i></sub>)<sup>α</sup>)<i>u</i> = 0 with finite Bloch norm || <i>u</i> ||<sub>${\cal B}$<sub>α</sub></sub>(σ) of a weight <i>t</i><sup>σ</sup>. It is known that ${\cal B}$<sub>1/2</sub>(0) coincides with the classical harmonic Bloch space on <i>H</i>. We extend the notion of harmonic conjugate functions to functions in the α-parabolic Bloch type space ${\cal B}$<sub>α</sub>(σ). We study properties of α-parabolic conjugate functions and give an application to the estimates of tangential derivative norms on ${\cal B}$<sub>α</sub>(σ). Inversion theorems for α-parabolic conjugate functions are also given.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 65(2), 487-520, 2013-04-01

    The Mathematical Society of Japan

References:  10

Codes

  • NII Article ID (NAID)
    10031177289
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    024428791
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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