Abstract
We prove that each translation and dilation invariant subspace X ⊂ L p(ℝn), X ≠ L p(ℝn), is contained in a maximal translation and dilation invariant subspace of L p(ℝn). Moreover, we prove that the set of all maximal translation and dilation invariant subspaces of L p(ℝn) has the power of continuum. Bibliography: 6 titles.
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