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arXiv · 2507.09723

Extending BMO functions in parabolic setting

N. V. Krylov
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Abstract

We prove that one can extend any $BMO^{x}$ function $a$ given in a cube in $\mathbb{R}^{d+1}$ to become a $BMO^{x}$ functions $\hat a$ in $\mathbb{R}^{d+1}$ almost preserving its $[a]^{\sharp}$ seminorm, which is, loosely speaking, $L_{\infty}$-norm of the maximal function in $t$ and $BMO$-norm in $x$.

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N. V. Krylov. 2025-07-13. Extending BMO functions in parabolic setting. https://arxiv.org/abs/2507.09723

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