Absolute continuity of quadratic variation of continuous local martingales

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I am interested to know if there are any simple sufficient conditions on continuous local martingale to have absolutely continuous quadratic variation. In general , we know only that quadratic variation is non-decreasing and continuous for continuous local martingales. I could not find any sufficient conditions for absolute continuity in standard text books like Karatzas and Shreve. Any help/reference is highly appreciated. Thanks