Abstract
The crucial point in the construction of an almost optimal decomposition for the couple (Lq, W kp ) was the covering theorem in which the parameter α (α-capacity) was controlled. Here we give a detailed proof of this theorem for negative α. Bibliography: 5 titles.
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References
N. Ya. Kruglyak, “Smooth analogs of Calderon-Zygmund decompositions, quantitative covering theorems, and theK-functional for the couple {\(\left( {L_q ,\dot W_p^k } \right)\)},”Algebra Analiz,8, 110–160 (1996).
N. Ya, Kruglyak, “Quantitative Whitney-type covering theorem,” {jtDokl. RAN}, {vn352}, {snNo. 1} ({dy1997}) {cm(to appear)}.
A. S. Besicovitch, “A general form of covering principle and relative differentiation of additive functions,”Proc. Cambridge Philos. Soc.,41, 103–110 (1945).
M. Guzman “Differentiability of integrals inRn,” Lect. Notes Math.,481 (1975).
H. Whitney, “Analytic extensions of differentiable functions defined in closed sets,”Trans. Am. Math. Soc.,36, 63–89 (1934).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 96–113.
Translated by S. V. Kislyakov.
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Kruglyak, N.Y. Quantitative Whitney-type theorems. J Math Sci 101, 3104–3114 (2000). https://doi.org/10.1007/BF02673735
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DOI: https://doi.org/10.1007/BF02673735