On weighted Hardy inequality with two-dimensional rectangular operator - extension of the E. Sawyer theorem

A characterization is obtained for those pairs of weights $v$ and $w$ on $\mathbb{R}^2_+$, for which the two--dimensional rectangular integration operator is bounded from a weighted Lebesgue space $L^p_v(\mathbb{R}^2_+)$ to $L^q_w(\mathbb{R}^2_+)$ for $1

Keywords:

• Combinatorics
• characterization
• Operator (physics)
• extension
• Complement (group theory)
• Bounded function
• Standard probability space
• Mathematics

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