One-sided median porosity of E is necessary and sufficient for d_E to the minus alpha to be in one-sided A_p for some alpha greater than zero when 1 less than p less than infinity, with new median characterizations of A_p and BMO.
Rubio de Francia.Weighted norm inequalities and related topics, volume 116 ofNorth-Holland Mathematics Studies
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One-sided median porous sets and one-sided Muckenhoupt distance functions
One-sided median porosity of E is necessary and sufficient for d_E to the minus alpha to be in one-sided A_p for some alpha greater than zero when 1 less than p less than infinity, with new median characterizations of A_p and BMO.