Regular compact factorization of integral operators in \(L_ p\). (English) Zbl 0558.45013

Korotkov, V. B.

Math. Notes 32, 785-788 (1983).

Translation from Mat. Zametki 32, No.5, 601-606 (Russian) (1982; Zbl 0537.45013)].

MSC:

45P05	Integral operators
47Gxx	Integral, integro-differential, and pseudodifferential operators
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47A68	Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47B38	Linear operators on function spaces (general)

Keywords:

regular and compact factorization; Lp-spaces; Nikishin’s theorem; representation of integral operators

Citations:

Zbl 0537.45013

References:

[1]	V. B. Korotkov, ?Integral and partially integral operators,? Sib. Mat. Zh.,19, No. 1, 70-90 (1978). · Zbl 0386.47013
[2]	E. M. Nikishin, ?Resonance theorems and superlinear operators,? Usp. Mat. Nauk,25, No. 6, 129-191 (1970). · Zbl 0222.47024
[3]	M. A. Krasnosel’skii, P. P. Zabreiko, E. I. Pustyl’nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).
[4]	B. Maurey, ?Theoremes de Nikishin: theoremes de factorisation pour les applications lineares a valeurs dans un espaces L0(?,?),? in: Seminaire Maurey-Schwartz, Espace LP, Applications Radonifiantes et Geometrie des Espaces de Banach, Ecole Polytechnique, Paris, 1972-1973, Exp. No. 12.
[5]	P. R. Halmos, Measure Theory, Van Nostrand, Princeton (1950).
[6]	N. Aronszajn and P. Szeptycki, ?On general integral transformations,? Math. Ann.,163, No. 2, 127-154 (1966). · Zbl 0171.12402 · doi:10.1007/BF02052846
[7]	S. Kaczmarsh and H. Steinhaus, Theory of Orthogonal Series [in German], Chelsea Publ.