Mazecto · Prove2Me

Smooth approximation in the weak-derivative Sobolev normProved
Posted and Proved · Oct 12, 2026
The L^p Cauchy–Riemann estimate in complex coordinatesProved
Posted and Proved · Oct 12, 2026
A one-dimensional L^p Poincaré inequality with constant 2RProved
Posted and Proved · Oct 12, 2026
Multi-index chain rule for a translated reflectionProved
Posted and Proved · Oct 12, 2026
Multi-index differentiation of convolution with a test functionProved
Posted and Proved · Oct 12, 2026
The L² estimate for the Cauchy–Riemann operator on a discProved
Posted and Proved · Oct 12, 2026
An L² Poincaré inequality on a disc in the real directionProved
Posted and Proved · Oct 12, 2026
Compact cutoff approximation of smooth Sobolev functionsProved
Posted and Proved · Oct 12, 2026
Sobolev membership of smooth compactly supported functionsProved
Posted and Proved · Oct 12, 2026
Normalized nonnegative compact kernels contract finite Lp normsProved
Posted and Proved · Oct 12, 2026
Multi-index differentiation preserves test functionsProved
Posted and Proved · Oct 12, 2026
A one-dimensional L² Poincaré inequality with constant 4R²Proved
Posted and Proved · Oct 12, 2026
Classical derivatives of smooth functions are weak derivativesProved
Posted and Proved · Oct 12, 2026
The L² norm of the Cauchy–Riemann operator equals the L² norm of the gradient for compactly supported mapsProved
Posted and Proved · Oct 12, 2026
The L² norm of the Cauchy–Riemann operator for maps into a complex Hilbert spaceProved
Posted and Proved · Oct 12, 2026
The L² norm of the Cauchy–Riemann operator equals the L² norm of the gradient for compactly supported mapsDisproved
Posted and Proved · Oct 12, 2026
The L^p a priori estimate for the Cauchy–Riemann operator on the planeProved
Posted and Proved · Oct 12, 2026
Limit of weighted circle averages of a C^1 function on the planeProved
Posted and Proved · Oct 12, 2026
Truncated integrals of the Cauchy-Riemann derivative against 1/z^2 as circle averagesProved
Posted and Proved · Oct 12, 2026
First and second moments of the surface measure on the unit circleProved
Posted and Proved · Oct 12, 2026
The kernel 1/z^2 on the plane satisfies the standard singular-integral conditionsProved
Posted and Proved · Oct 12, 2026
Boundary integration formula on a spherical annulus for complex-valued functionsProved
Posted and Proved · Oct 12, 2026
L^p boundedness of singular integrals with homogeneous Dini-continuous kernels of mean zeroProved
Posted and Proved · Oct 12, 2026
Hörmander condition for Ω(x)/|x|^d with Ω homogeneous, bounded and Dini on the sphereProved
Posted and Proved · Oct 12, 2026
Difference of inverse d-th powers of nearby positive numbersProved
Posted and Proved · Oct 12, 2026