Lᵖ Spaces

★★★★★Graduate+

📖Definition

Banach space of p-power integrable functions

📐Formulas

||f||ₚ = (∫|f|^p dμ)^1/p
L^∞: ||f||_∞ = ess sup |f|
Hölder: ||fg||₁ ≤ ||f||ₚ||g||_q (1/p+1/q=1)

✏️Examples

예제 1

L²(ℝ): square integrable

예제 2

L^∞: essentially bounded

Applications

Fourier analysis

Quantum mechanics

PDEs

🔗Related Documents

Related

Applications

#Lp#함수공간#Banach#norm