Inclusion relations for the spaces L(ℝ), \mathcal{H}\mathcal{K}(ℝ) ∩ \mathcal{B}\mathcal{V}(ℝ), and L2(ℝ)

The inclusion relations for the spaces \( \mathcal{H}\mathcal{K} \)(I), L(I), \( \mathcal{H}\mathcal{K} \)(I) ∩ \( \mathcal{B}\mathcal{V} \) (I), and L 2(I) are found. On unbounded intervals, functions in \( \mathcal{H}\mathcal{K} \)(I) ∩ \( \mathcal{B}\mathcal{V} \) (I) need not be Lebesgue integrable.