scability9087 scability9087

06-06-2023
Mathematics

contestada

1. Let u be the lebesgue measure in R, = (0,00) and let p € (1,00). Show that the function f defined by f(x) = x²(1 + [log x])=¹ for x € R, that belong to the Lebesgue space LP (R₂) for p € (1,00) if and only if p = 2. Compute the norm ||/\|(₂).

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