On boundedness of operators of weak type $$$(\varphi_0, \psi_0, \varphi_1, \psi_1)$$$ in Lorentz spaces in limit cases

B.I. Peleshenko (Dnipropetrovsk State Agrarian University)


We prove theorems on boundedness of operators of weak type $$$(\varphi_0, \psi_0, \varphi_1, \psi_1)$$$ from Lorentz space $$$\Lambda_{\varphi,a}(\mathbb{R}^n)$$$ to $$$\Lambda_{\varphi,b}(\mathbb{R}^n)$$$ in “limit” cases, when one of functions $$$\varphi(t) / \varphi_0(t)$$$, $$$\varphi(t) / \varphi_1(t)$$$ slowly changes at zero and at infinity.


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DOI: https://doi.org/10.15421/240716



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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991