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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces

Ömer Faruk DOĞAN
Sayfa
811–820
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into harmonic Bergman-Besov spaces $b^{q}_{\beta}$, weighted Bloch spaces $b^{\infty}_{\beta} $ or the space of bounded harmonic functions $h^{\infty}$, allowing the exponents to be different.
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Temel Bulgular & Veri:We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into harmonic Bergman-Besov spaces $b^{q}_{\beta}$, weighted Bloch spaces $b^{\infty}_{\beta} $ or the space of bounded harmonic functions $h^{\infty}$, allowing the exponents to be different.
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Sonuç & Katkı:These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:integral operator · harmonic Bergman-Besov kernel · harmonic Bergman-Besov space

Abstract

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into harmonic Bergman-Besov spaces $b^{q}_{\beta}$, weighted Bloch spaces $b^{\infty}_{\beta} $ or the space of bounded harmonic functions $h^{\infty}$, allowing the exponents to be different. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.

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Bu Makaleye Atıf Yap

DOĞAN, Ö. F. (2022). A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 811–820. https://ajindex.com/articles/529516

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Kaynakça (12)

  1. S. Axler, P. Bourdon and W. Ramey, Harmonic function theory, 2nd ed., Grad. Texts in Math., 137, Springer, New York, 2001
  2. A.E. Djrbashian and F.A. Shamoian, Topics in the Theory of $A^{p}_{\alpha}$ Spaces, Teubner Texts in Mathematics 105, Leipzig, 1988
  3. Ö.F. Doğan, Harmonic Besov spaces with small exponents, Complex Var. Elliptic Equ. 65 (6), 1051–1075, 2020
  4. Ö.F. Doğan, A Class of Integral Operators Induced by Harmonic Bergman-Besov Kernels on Lebesgue Classes, arXiv:2002.03193v2 [math.CA], 2020
  5. Ö.F. Doğan and A.E. Üreyen, Weighted harmonic Bloch spaces on the ball, Complex Anal. Oper. Theory 12 (5), 1143–1177, 2018
  6. S. Gergün, H.T. Kaptanoğlu and A.E. Üreyen, Reproducing kernels for harmonic Besov spaces on the ball, C. R. Math. Acad. Sci. Paris 347, 735–738, 2009
  7. S. Gergün, H.T. Kaptanoğlu and A.E. Üreyen, Harmonic Besov spaces on the ball, Int. J. Math. 27 (9), 1650070, 59 pp., 2016
  8. M. Jevtić and M. Pavlović, Harmonic Bergman functions on the unit ball in $\mathbb R^n$, Acta Math. Hungar. 85, 81–96, 1999
  9. M. Jevtić and M. Pavlović, Harmonic Besov spaces on the unit ball in $\mathbb R^n$, Rocky Mountain J. Math. 31, 1305–1316, 2001
  10. H.T. Kaptanoğlu and A.E. Üreyen, Singular integral operators with Bergman-Besov kernels on the ball, Integr. Equ. Oper. Theory 91, 30 pp., 2019
  11. S. Pérez-Esteva, Duality on vector-valued weighted harmonic Bergman spaces, Studia Math. 118, 37–47, 1996
  12. K. Stroethoff, Harmonic Bergman spaces, in Holomorphic Spaces, Mathematical Sciences Research Institute Publications, 33, Cambridge University, Cambridge, 51– 63, 1998