Question

Show that $N(f)= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(\mathbb{R}), h \in L^q(\mathbb{R})\}$ is a norm on $L^p(\mathbb{R})+L^q(\mathbb{R}) $

score 76 · Answer 1 · 2026-04-15 17:41:05

76

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Show that $N(f)= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(\mathbb{R}), h \in L^q(\mathbb{R})\}$ is a norm on $L^p(\mathbb{R})+L^q(\mathbb{R}) $

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162

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462

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139

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List Question

Show that $N(f)= \inf\{\|g\|_p+\|h\|_q;f=g+h, g \in L^p(\mathbb{R}), h \in L^q(\mathbb{R})\}$ is a norm on $L^p(\mathbb{R})+L^q(\mathbb{R}) $

Formula for simple interest calculation but with added base fee

Compacting a number scale using a logarithmic function

Find polynomial $q(x)$ whose values match a known polynomial $p(x)$ with matching values except one.

interpolation in multiobjective optimization of linear functions

Is step-wise interpolation possible for a curve which cannot be represented by a function?

How to prove $\|P|X|^\theta\|_{p/\theta} \le \|P|X|\|_p^{\theta}$

Proving second differences

Do I interpolate a polynomial using derivatives instead of divided differences correctly?

Deducing an interpolation inequality from another interpolation inequality

What is the formula to set up a generalized Vandermonde matrix?

Mathematical function for a gradually falling parabolic curve in 1st quadrant

A question on Interpolation..

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Calculate length of curve created by interpolation of polar coordinates

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