ESTONIAN ACADEMY
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Proceedings of the Estonian Academy of Sciences. Physics. Mathematics
Calderón–Zygmund type decompositions and applications; pp. 170–173
PDF | https://doi.org/10.3176/phys.math.2006.3.07

Author
Natan Kruglyak
Abstract

In the paper a variant of the abstract approach to the Calderón–Zygmund type decompositions is considered. Applications to K-closedness of spaces of analytic functions are given.

References

1. Calderón, A. P. and Zygmund, A. On the existence of certain singular integrals. Acta Math., 1952, 88, 85–139. 
https://doi.org/10.1007/BF02392130

2. Kislyakov, S. and Kruglyak, N. Stability of approximation under singular integral operators and Calderón–Zygmund type decompositions. Preprint 07/2005, St. Peters- burg Steklov Mathematical Institute

3. Kislyakov, S. and Kruglyak, N. Stability of approximation under singular integral operators and Calderón–Zygmund type decompositions II. ESI Preprint 1734, 2005

4. Krugljak, N. Smooth analogs of Calderón–Zygmund decompositions, quantitative covering theorems and K -functional for the couple (Lq , Ẇpk ). Algebra i Analiz, 1996, 8, 110–160 (in Russian); English translation in St. Petersburg Math. J., 1997, 8, 617– 649. 

5. Krugljak, N. Quantitative theorems on Whitney-type coverings, In Investigations on Linear Operators and Function Theory25, 96–113; Zap. Nauchn. Sem. St. Petersburg Otdel. Math. Inst. im. Steklova (POMI), 1997, 247 (in Russian). English translation in J. Math. Sci. (New York), 2000, 101, 3104–3114. 
https://doi.org/10.1007/BF02673735

6. Kruglyak, N. and Kuznetsov, E. Smooth and nonsmooth Calderón–Zygmund type decompositions for Morrey spaces. J. Fourier Anal. Appl., 2005, 11, 697–714. 
https://doi.org/10.1007/s00041-005-5032-7

7. Pisier, G. Interpolation between Hp spaces and noncommutative generalizations. I. Pacific J. Math., 1992, 155, 341–368. 
https://doi.org/10.2140/pjm.1992.155.341

 

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