A weighted weak-type inequality for the one-sided maximal operators
Abstract
UDC 517.5
We obtain some necessary and sufficient conditions for a weighted weak-type inequality of the form $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widetilde{\varphi}\left(C_{1}\frac{|f(x)|}{\omega_{1}(x)\omega_{2}(x)}\right)\omega_{2}(x)\,dx$$ to be true, which generalize some known results.
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