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

doi:10.15421/240815

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)

Abstract

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 $$$\left( \Lambda_{\psi_1 \infty}(\mathbb{R}^n), \Lambda_{\psi_2 \infty}(\mathbb{R}^n) \right)$$$.

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