For fractional Kolmogorov semigroups, the rho-variation operators with rho>2 are bounded on L^p exactly for p>1∨d/beta, while the 2-variation operator is never bounded from L^p to weak L^p.
J., and Rodr\' guez-Mesa, L
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Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators
For fractional Kolmogorov semigroups, the rho-variation operators with rho>2 are bounded on L^p exactly for p>1∨d/beta, while the 2-variation operator is never bounded from L^p to weak L^p.