Which fashion brand under LVMH was established by designer Marc Jacobs?

Marc Jacobs is indeed the fashion brand established by designer Marc Jacobs himself. This label reflects his vision and creativity, making it distinct from the other brands listed, which are separately established by different designers or entities.

Louis Vuitton, while a significant brand within LVMH, was founded long before Marc Jacobs joined as the artistic director and is part of a long heritage of luxury leather goods. Christian Dior, another prestigious brand under LVMH, was founded by Christian Dior himself in 1946, long before Marc Jacobs ventured into the fashion world. Kenzo, known for its vibrant designs, was established by Kenzo Takada and does not relate directly to Marc Jacobs.

The establishment of the Marc Jacobs brand showcases his contributions to the fashion industry, including the synthesis of street style with high fashion, which has left a notable impact within the fashion landscape.