Lawrence

Here is the set up in question: ( I will only address the imediate area and not identify the surrounding pieces) White advances from g2 to g4 - black pawn is on h4. Normally as I understand it black pawn may now advance diagonally to take white pawn to advance to g3. Now here is my question: Can this be accomplished only if there is an open space on h3? Since in this scenario the white pawn is occupying h3, does this space being occupied prevent the En Passant to be accomplished? Thank you, Lawrence