I think Louis Vuitton was inspired by Felix's Magical Bag.
I knew exactly what a Bag of Holding was, but I had never heard that term before! According to Wikipedia, a Bag of Holding is "a fictional magical item in the Dungeons & Dragons roleplaying game, capable of containing obects larger than it's own size. Since it's introduction, it has appeared in other roleplaying games and media." Now, D&D may have coined the term, but it didn't invent the concept of a bag or space that can contain more than it should be capable of. According to tvtropes.org, a Bag of Holding is "a specific portable item which is bigger on the inside than it is on the outside. Much bigger. It may not look it, but that's because it contains Hammer Space. Because the holding capacity of the bag comes from internal Hammer Space, a thoroughly-packed Bag of Holding will weigh no more than a full normal bag. Odds are, it will weigh no more than an empty normal bag".
Upon learning the trope of this concept I thought of Felix the Cat and his Magical Bag of Tricks:
And there's Mary Poppins:
Jessica Rabbit has a Victoria's Secret Compartment to keep anyone from frisking her:
Here's another Victoria's Secret Compartment.
Hammer Space is the space within a Bag of Holding is anywhere that items can be stored and accessed from and where they go back to when not in use. It's common for cartoons and anime/manga characters to pull a hammer seemingly from nowhere to smack another character with. I have always appreciated and accepted Hammer Space. It exists often from behind a person's back or from behind thin things such as trees and lampposts. Even hair can contain Hammer Space. Hammer Space could exist potentially anywhere so long as it is hidden from view before and perhaps while the item (or hammer) is accessed. From within clothing is a common place for Hammer Space.
I appreciate this trope so much because it is a very accepted notion in film and games and it is used for fantastic comedic effect. Cartoons do what real life cannot. Live action film certainly has the power to do as real life cannot but typically more "realistic" expectations are put upon live-action film. When a live-action film acts "cartoony" and allows the impossible to be believed and experienced such as in Kung Fu Hustle, Raising Arizona or Scott Pilgrim Vs. The World; the effect is thrilling.
Some more examples of Hammer Space / Bags of Holding:
Bender's chest compartment (Futurama)
Baby Herman (in Tummy Trouble) (*see this short at the 1 minute and 46 second mark!)
The Tardis (Dr. Who)
Marge Simpson's hair (The Simpsons)
Ramona Flowers' bag (Scott Pilgrim Vs. the World)
Yakko Warner's bag (Animaniacs)