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Matematicheskie Zametki, 2004, Volume 75, Issue 4, Pages 580–591
DOI: https://doi.org/10.4213/mzm52 (Mi mzm52) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Strong-Type Inequality for Convolution with Square Root of the Poisson Kernel

V. G. Krotova, I. N. Katkovskaya

a Belarusian State University, Faculty of Mathematics and Mechanics
Full-text PDF (236 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm52
Abstract: The boundary behavior of convolutions with Poisson kernel and with square root of the Poisson kernel is essentially different. The former has only a nontangential limit. The latter involves convergence over domains admitting the logarithmic order of tangency with the boundary (P. Sjögren, J.-O. Rönning). This result was generalized by the authors to spaces of homogeneous type. Here we prove the boundedness in Lp, p>1, of the corresponding maximal operator. Only a weak-type inequality was known before.
Received: 23.06.2003
English version:
Mathematical Notes, 2004, Volume 75, Issue 4, Pages 542–552
DOI: https://doi.org/10.1023/B:MATN.0000023335.53027.30
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: V. G. Krotov, I. N. Katkovskaya, “Strong-Type Inequality for Convolution with Square Root of the Poisson Kernel”, Mat. Zametki, 75:4 (2004), 580–591; Math. Notes, 75:4 (2004), 542–552
Citation in format AMSBIB
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\pages 580--591
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\transl
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\pages 542--552
\crossref{https://doi.org/10.1023/B:MATN.0000023335.53027.30}
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  • https://doi.org/10.4213/mzm52
  • https://www.mathnet.ru/eng/mzm/v75/i4/p580
    • This publication is cited in the following 4 articles:
    1. Safaryan M.H., “On Generalizations of Fatou'S Theorem in l-P For Convolution Integrals With General Kernels”, J. Geom. Anal., 31:4 (2021), 3280–3299  crossref  mathscinet  isi
    2. G. A. Karagulyan, I. N. Katkovskaya, V. G. Krotov, “The Fatou Property for General Approximate Identities on Metric Measure Spaces”, Math. Notes, 110:2 (2021), 196–209  mathnet  crossref  crossref  isi  elib
    3. Karagulyan G.A., Safaryan M.H., “on a Theorem of Littlewood”, Hokkaido Math. J., 46:1 (2017), 87–106  crossref  mathscinet  zmath  isi  scopus
    4. Karagulyan G.A., Safaryan M.H., “On Generalizations of Fatou'S Theorem For the Integrals With General Kernels”, J. Geom. Anal., 25:3 (2015), 1459–1475  crossref  mathscinet  zmath  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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