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2009•Journal of MathematicsRequires access

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

Zhou Shujuan

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Abstract

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 H1,∞atb(μ) to L1(μ) and from L∞(μ) to RBMO(μ) for non-doubling measure. Hence we prove that these operators are bounded on Lp(μ),1p∞. These results extend the boundedness of the Calderon-Zygmund operators on spaces for doubling measures.

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What this paper is about

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 H1,∞atb(μ) to L1(μ) and from L∞(μ) to RBMO(μ) for non-doubling measure. Hence we prove that these operators are bounded on Lp(μ),1p∞. These results extend the boundedness of the Calderon-Zygmund operators on spaces for doubling measures.

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Available abstract

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 H1,∞atb(μ) to L1(μ) and from L∞(μ) to RBMO(μ) for non-doubling measure. Hence we prove that these operators are bounded on Lp(μ),1p∞. These results extend the boundedness of the Calderon-Zygmund operators on spaces for doubling measures.

Key concepts: Mathematics, Bounded function, Measure (data warehouse), Singular integral operators, Type (biology), Pure mathematics, Discrete mathematics, Operator theory

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