Without a photo, I'm just guessing, but it could be mealy bugs -- a sucking insect related to scale insects that covers/protects itself with white cottony looking waxy substance. Try touching them with cotton swab soaked in rubbing alcohol. If mealy bug, it should wipe off with orangish-red smear. if so, proceed to remove them with the alcohol and swabs.
Palms tend to need more light than you might think as they look OK but slowly deteriorate in less than ideal light conditions.
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