• Q X Yang

      Articles written in Proceedings – Mathematical Sciences

    • Lp-continuity for Calderón-Zygmund operator

      Q X Yang

      More Details Abstract Fulltext PDF

      Given a Calderón-Zygmund (C-Z for short) operatorT, which satisfies Hörmander condition, we prove that: ifT maps all the characteristic atoms toWL1, thenT is continuous fromLp toLp(1 <p < ∞). So the study of strong continuity on arbitrary function inLp has been changed into the study of weak continuity on characteristic functions.

    • Wavelet characterization of Hörmander symbol classSρ,δm and applications

      Q X Yang

      More Details Abstract Fulltext PDF

      In this paper, we characterize the symbol in Hormander symbol classSρm,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kerneldistribution property for the symbol in the symbol classSρm,δ (mR, ρ > 0, δ 0) which is more general than known results ; for non-regular symbol operators, we establish sharp L2-continuity which is better than Calderón and Vaillancourt’s result, and establishLp (1 ≤p ≤∞) continuity which is new and sharp. Our new idea is to analyse the symbol operators in phase space with relative wavelets, and to establish the kernel distribution property and the operator’s continuity on the basis of the wavelets coefficients in phase space.

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