$frac1p+frac1q=1$ vs $sum_n=0^infty frac1p^n=q$
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It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
also satisfy the relations:
- $sum_n=0^infty frac1p^n=q;$
- $sum_n=0^infty frac1q^n=p.$
I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?
real-analysis soft-question
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up vote
6
down vote
favorite
It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
also satisfy the relations:
- $sum_n=0^infty frac1p^n=q;$
- $sum_n=0^infty frac1q^n=p.$
I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?
real-analysis soft-question
add a comment |Â
up vote
6
down vote
favorite
up vote
6
down vote
favorite
It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
also satisfy the relations:
- $sum_n=0^infty frac1p^n=q;$
- $sum_n=0^infty frac1q^n=p.$
I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?
real-analysis soft-question
It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
also satisfy the relations:
- $sum_n=0^infty frac1p^n=q;$
- $sum_n=0^infty frac1q^n=p.$
I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?
real-analysis soft-question
asked Aug 7 at 21:27
Bob
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1,489522
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