θ(t)型Calderón-Zygmund算子在非双倍测度下的有界性(英文)

BOUNDEDNESS OF θ(t) TYPE CALDERóN-ZYGMUND OPERATORS FOR NON-DOUBLING MEASURE

本文研究了奇异积分算子在非双倍测度下的有界性问题,利用原子分解理论,证明了θ(t)型Calderón-Zygmund算子在非双倍测度下是从Hatb1,∞(μ)到L1(μ)以及从L∞(μ)到RBMO(μ)有界的.这样,推广了Calderón-Zygmund算子在双倍测度下的空间有界性.

In this paper, we discuss the boundedness of singular integral operators on non- doubling measure. By the atomic decompositions, we get that the θ（t） type Calderon-Zygmund operators are bounded from Hatb^1,∞ （μ） to L^1 （μ） and from L^∞ （μ） to RBMO（μ） for non-doubling measure. Hence we prove that these operators are bounded on L^p （μ）, 1〈p〈∞. These results extend the boundedness of the Calderon-Zygmund operators on spaces for doubling measures.