Bilinear decompositions for the product space H¹_L× BMO_L

2012/04/13 by Luong Dang Ky, Ky, Luong Dang
Mathematics · #35J10 #42B35 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1204.3041

openalex publication_date 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we improve a recent result by Li and Peng on products of functions in H_L¹(\bR^d) and BMO_L(\bR^d), where L=-Δ+V is a Schrödinger operator with V satisfying an appropriate reverse Hölder inequality. More precisely, we prove that such products may be written as the sum of two continuous bilinear operators, one from H_L¹(\bR^d)× BMO_L(\bR^d) into L¹(\bR^d), the other one from H¹_L(\bR^d)× BMO_L(\bR^d) into H^log(\bR^d), where the space H^log(\bR^d) is the set of distributions f whose grand maximal function \mathfrak Mf satisfies ∫_{\mathbb R^d} \frac |\mathfrak M f(x)|log (e+ |\mathfrak Mf(x)|)+ log(e+|x|)dx

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