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2017•Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)Requires access

Commutators of homogeneous fractional integrals on Herz-type Hardy spaces with variable exponent

Hongbin Wang

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Abstract

Let Ω ∈ L s (S n−1), s ≥ 1, be a homogeneous function of degree zero, and let σ (0 < σ < n) and b be Lipschitz or BMO functions. In this paper, we establish the boundedness of the commutators [b, T Ω,σ ], generated by a homogeneous fractional integral operator T Ω,σ and function b, on the Herz-type Hardy spaces with variable exponent.

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Let Ω ∈ L s (S n−1), s ≥ 1, be a homogeneous function of degree zero, and let σ (0 < σ < n) and b be Lipschitz or BMO functions. In this paper, we establish the boundedness of the commutators [b, T Ω,σ ], generated by a homogeneous fractional integral operator T Ω,σ and function b, on the Herz-type Hardy spaces with variable exponent.

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Available abstract

Let Ω ∈ L s (S n−1), s ≥ 1, be a homogeneous function of degree zero, and let σ (0 < σ < n) and b be Lipschitz or BMO functions. In this paper, we establish the boundedness of the commutators [b, T Ω,σ ], generated by a homogeneous fractional integral operator T Ω,σ and function b, on the Herz-type Hardy spaces with variable exponent.

Key concepts: Mathematics, Lipschitz continuity, Homogeneous, Type (biology), Exponent, Hardy space, Mathematical analysis, Maximal function

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