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Improved fractional Poincaré type inequalities in John domains
We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient ...
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...