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Criteria of general weak type inequalities for integral transforms with positive kernels

Authors:

I Genebashvili A Gogatishvili V Kokilashvili

Institution:

1. A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1 Z. Rukhadze St., 380093, Tbilisi, Republic of Georgia

Abstract:

Necessary and sufficient conditions are derived in order that an inequality of the form

$\begin{gathered} \varphi (\lambda )\theta (\beta \{ (x,t) \in X x (0,\infty ):\kappa (fdv)(x,t) > \lambda \} ) \leqslant \hfill \\ \leqslant c\int\limits_X {\psi \left( {\frac{{f(x)}}{{\eta (\lambda )}}} \right)\sigma (x)dv(x)} \hfill \\ \end{gathered}$

Keywords:	1991 Mathematics Subject Classification" target="_blank">1991 Mathematics Subject Classification 42B25 26D15 46E30
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