At the moment, there’s no state-wide answer, because the state Supreme Court has not ruled on the matter, and two appellate courts in different appellate districts have reached contrary conclusions.
Here’s the context: The state is divided into six appellate districts, each of which covers a specific set of counties. When a court in one appellate district rules one way on a question, the trial courts in its group are bound by that interpretation. But trial courts in other appellate districts are not required to follow that lead (though they often give it great deference), and if another appellate court in a different district reaches a contrary result, the trial judges in its group must follow its conclusion. Trial courts in counties whose appellate courts have not ruled on the matter are free to follow either. So as you can see, if appellate courts disagree and some are silent, the result in any superior court case will depend on where, district-wise, the superior court is situated. (You can see which counties fit into which appellate districts at the Courts of Appeal home page – click the link to your area for a precise list of covered counties.)
Such is the situation with the question posed above. The Fourth District Court of Appeal allowed a trial judge to resentence a defendant while the defendant’s appeal was pending; but the Third District did not, ruling that the defendant had to wait until the appeal was concluded (People v. Awad, 2015 DJDAR 7588 (Fourth District); People v. Scarbrough, 2015 DJDAR 10942 (Third District).) The courts disagreed as to whether the trial court, having handed the case up to the appellate court, had any jurisdiction, or right, to continue to act.
When appellate decisions clash like this, the state Supreme Court typically resolves the dispute and makes law for the entire state. But in the meantime, a defendant’s chances of resentencing pending an appeal will depend on the location of the trial court.