Trenitalia luggage allowance
Trenitalia describes what you can bring instead of publishing measurements. Their rule is shown below in their own words, and never turned into a yes or no.
What Trenitalia says
Trenitalia, in their own words
Passengers may take luggage or other easily transportable items (such as strollers, prams, high chairs if foldable, umbrellas, deckchairs, skis, musical instruments) on board the coach free of charge, provided they are stored in the spaces made available for luggage. Luggage may be permitted to exceed this volume limit as long as it does not disturb or cause injury to other passengers, does not obstruct railway staff from carrying out their work, and does not damage the coach. On some trains, specific spaces have been made available for passengers to store larger luggage items. Trenitalia's Conditions of Carriage (SCIC-NRT, section 14) add that each passenger may take no more than three easy-to-handle items as hand luggage, and refer to each carrier's own conditions for exact maximum measurements. Note: the wording above refers to a volume limit that Trenitalia does not state on this page.
Before you rely on this
An empty field on this page means the operator doesn't publish that figure. It never means there is no limit.
Meeting a published limit is not a promise that staff will accept your bag at the gate. At least one operator states that paying at the gate does not guarantee a bag over the limit will be carried.