OpenAI reports an endpoint gradient bound for centered disk averages
- Mathematics
For every real f in W¹,¹(R²), the centered-disk maximal function has a globally integrable weak gradient and satisfies ||∇Mf||₁ ≤ C||∇f||₁ for an absolute constant C.
OpenAI reports an endpoint gradient bound for centered disk averages
- Mathematics
For every real f in W¹,¹(R²), the centered-disk maximal function has a globally integrable weak gradient and satisfies ||∇Mf||₁ ≤ C||∇f||₁ for an absolute constant C.
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Understand the problem ↓Understanding the problem
Read the background
For every real f in W¹,¹(R²), the centered-disk maximal function has a globally integrable weak gradient and satisfies ||∇Mf||₁ ≤ C||∇f||₁ for an absolute constant C.
Why it matters
If correct, resolves the planar centered-disk case of a longstanding Sobolev endpoint question.
What counts as progress
Does the centered disk maximal operator preserve an L¹ gradient bound on W¹,¹(R²)?
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OpenAI reports an endpoint gradient bound for centered disk averages