Geodesic
On the Marcinkiewicz--Calder\'on Interpolation Theorem for Integral Operators
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 422-432.

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The inverse problem to the classical Marcinkiewicz–Calderón interpolation theorem is considered. Necessary conditions for the Marcinkiewicz–Calderón theorem to hold for the integral operator under consideration are obtained in terms of the kernel of this operator. It is shown that these conditions are sufficient for the given integral operator to be of $(p,q)$-strong type for the same parameters $p$ and $q$ that appear in the interpolation theorem.
Keywords: integral operators, Marcinkiewicz interpolation theorem. 
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E. D. Nursultanov; N. T. Tleukhanova; Z. M. Mukeyeva. On the Marcinkiewicz--Calder\'on Interpolation Theorem for Integral Operators. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 422-432. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a8/

[1] I. Berg, I. Lefstrem, Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980 | MR | Zbl

[2] A. G. Kostyuchenko, E. D. Nursultanov, “Ob integralnykh operatorakh v $L_p$-prostranstvakh”, Fundament. i prikl. matem., 5:2 (1999), 475–491 | MR | Zbl

[3] E. D. Nursultanov, S. Tikhonov, “Net spaces and boundedness of integral operators”, J. Geom. Anal., 21:4 (2011), 950–981 | DOI | MR | Zbl

[4] S. Yano, “An extrapolation theorem”, J. Math. Soc. Japan, 3 (1951), 296–305 | MR | Zbl

[5] M. Milman, Extrapolation and Optimal Decompositions: With Applications to Analysis, Lecture Notes in Math., 1580, Springer-Verlag, Berlin, 1994 | DOI | MR | Zbl

[6] S. V. Astashkin, “Novye ekstrapolyatsionnye sootnosheniya v shkale $L_p$-prostranstv”, Funkts. analiz i ego pril., 37:3 (2003), 73–77 | DOI | MR | Zbl

[7] S. V. Astashkin, K. V. Lykov, “Ekstrapolyatsionnoe opisanie prostranstv Lorentsa i Martsinkevicha, “blizkikh” k $L_\infty$”, Sib. matem. zhurn., 47:5 (2006), 974–992 | MR | Zbl

[8] E. I. Berezhnoi, A. A. Perfilev, “Tochnaya teorema ekstrapolyatsii dlya operatorov”, Funkts. analiz i ego pril., 34:3 (2000), 66–68 | DOI | MR | Zbl