Characterization in terms of K-functionals of quasilinear operators of weak types $$$\left( \Lambda_{\varphi_0, 1}, \Lambda_{\psi_0, \infty} \right)$$$, $$$\left( \Lambda_{\varphi_1, 1}, \Lambda_{\psi_1, 1} \right)$$$

B.I. Peleshenko (Dnipropetrovsk State Agrarian University)


We obtain necessary and sufficient condition in terms of K-functionals of pairs of Lorentz spaces for quasilinear operator to act boundedly from pair of Lorentz spaces $$$\left( \Lambda_{\varphi_1 1}(\mathbb{R}^n), \Lambda_{\varphi_2 1}(\mathbb{R}^n) \right)$$$ to pair of Lorentz spaces $$$\left( \Lambda_{\psi_1 \infty}(\mathbb{R}^n), \Lambda_{\psi_2 \infty}(\mathbb{R}^n) \right)$$$.


Berg J., Lofstrom J. Interpolation of spaces. Introduction, 1980. (in Russian)

Dmitriev V.I. "To interpolation theorem", Dokl. AN SSSR, 1974; 215(3): pp. 518-521. (in Russian)

Krein S.G., Petunin Yu.I., Semyonov Ye.M. Interpolation of linear operators, Nauka, Moscow, 1978; 400 p. (in Russian)

Natanson I.P. Theory of real variable functions, Nauka, Moscow, 1974. (in Russian)

Peleshenko B.I. "On operators of weak type $$$(\phi_0, \psi_0, \phi_1, \psi_1)$$$", Works of Ukrainian Math. Congress-2001. Functional Analysis, Kyiv, 2002; pp. 234-244. (in Russian)

Bennett C., Rudnick K. On Lorentz-Zygmund spaces, Warszava, Panstw. wydawn. nauk., 1980; 73 p.

Holmstedt T. "Interpolation of quasi-normed spaces", Math. Scand., 1970; 26: pp. 177-199.

Lorentz G.G., Shimogaki T.J. "Interpolation theorems for operators in function spaces", J. Funct. Anal., 1968; 2: pp. 31-51. doi:10.1016/0022-1236(68)90024-4

Peetre J. "Nouvelles propriétés d'éspaces d'interpolation", C.R. Acad. Sci. Paris, 1963; 256: pp. 1424-1426. (in French)


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