What are examples of ORTHOGONAL function space for multivariable functions?

Question

• What are examples of orthogonal spaces of multivariable functions?

I asked a question and learned that $$\langle f(x_1,x_2,\cdots x_n),g(x_1,x_2,\cdots x_n) \rangle = \idotsint_D f(x_1,x_2,\cdots x_n) \overline{g(x_1,x_2,\cdots x_n)} dx_1dx_2\cdots dx_n$$.