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
→Prerequisites
←Next Topics
↔Related
⚡Applications
#Lp#함수공간#Banach#norm