Extending BMO functions in parabolic setting

2025/07/13 by Н. В. Крылов, Krylov, N. V. · 1 citation
Mathematics · #26E99 #42B37 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2507.09723

openalex publication_date 2025/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Essentials of Real Analysis and Morrey-Sobolev spaces for second-order elliptic and parabolic PDEs with singular first-order coefficients
• On two weight estimates for iterated commutators

Cited by

• On solvability of parabolic equations with singular coefficients in odd mixed-norm Morrey-Sobolev spaces
• Approximation of the Solutions to Quasilinear Parabolic Problems with Perturbed VMO_x Coefficients

Related

• Sharp L^p estimates on BMO
• BMO on shapes and sharp constants
• Extension theorem for bmo in a domain
• BMOA estimates and radial growth of B_ϕ functions
• Maximal operators on spaces BMO and BLO