This analysis extends BMO functions in a parabolic setting, suggesting new approaches to maintain their seminorm.
We prove that one can extend any BMOˣ function a given in a cube in Rᵈ⁺¹ to become a BMOˣ functions a in Rᵈ⁺¹ almost preserving its [a]^ seminorm, which is, loosely speaking, L∞-norm of the maximal function in t and $BMO$-norm in x.
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Н. В. Крылов (2025) studied this question.
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