Geodesic
A class of integral operators induced by harmonic Bergman-Besov kernels on Lebesgue classes
Filomat, Tome 36 (2022) no. 13, p. 4293

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DOI

We provide a full characterization in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with standard weights on the unit ball of R n. These operators in some sense generalize the harmonic Bergman-Besov projections. To obtain the necessity conditions, we use a technique that heavily depends on the precise inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball. This fruitful technique is new. It has been used first with holomorphic Bergman-Besov kernels by Kaptanoğlu and Üreyenand and Üreyen. Methods of the sufficiency proofs we employ are Schur tests or H ¨ older or Minkowski type inequalities which also make use of estimates of Forelli-Rudin type integrals.
DOI : 10.2298/FIL2213293D
Classification : 47B34, 47G10, 31B05, 31B10, 42B35, 45P05, 47B32, 46E20, 46E15
Keywords: Integral operator, Harmonic Bergman-Besov kernel, Harmonic Bergman-Besov space, Weighted harmonic Bloch space, Harmonic Bergman-Besov projection, Schur test, Forelli-Rudin estimate, Inclusion relation 
Ömer Faruk Doğan. A class of integral operators induced by harmonic Bergman-Besov kernels on Lebesgue classes. Filomat, Tome 36 (2022) no. 13, p. 4293 . doi: 10.2298/FIL2213293D
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     author = {\"Omer Faruk Do\u{g}an},
     title = {A class of integral operators induced by harmonic {Bergman-Besov} kernels on {Lebesgue} classes},
     journal = {Filomat},
     pages = {4293 },
     year = {2022},
     volume = {36},
     number = {13},
     doi = {10.2298/FIL2213293D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2213293D/}
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