Hardy–Stein identities and square functions for semigroups
Hardy–Stein identities and square functions for semigroups
We prove a Hardy–Stein-type identity for the semigroups of symmetric, pure-jump Lévy processes. Combined with the Burkholder–Gundy inequalities, it gives the L p two-way boundedness, for 1 < p < ∞ , of the corresponding Littlewood–Paley square function. The square function yields a direct proof of the L p -boundedness …