Singular integral operators, john–nirenberg inequalities and triebel–lizorkin type spaces on weighted lebesgue spaces with variable exponents

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Abstract

We establish the boundedness of singular integral operators, the Fefferman–Stein inequality and the John–Nirenberg inequalities on weighted Lebesgue spaces with variable exponents by using the extrapolation theorem. Moreover, as a consequence of the extrapolation theorem, we have the Fefferman–Stein vector-valued inequalities on weighted Lebesgue spaces, and hence we use it to study the weighted Triebel–Lizorkin spaces with variable exponent. Copyright © 2016 Unión Matemática Argentina.
Original languageEnglish
Pages (from-to)85-101
JournalRevista de la Unión Matemática Argentina
Volume57
Issue number1
Early online dateMar 2016
Publication statusPublished - 2016

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Weighted Lebesgue Spaces
Operator Inequality
Variable Exponent
Singular Integral Operator
Extrapolation
Triebel-Lizorkin Space
Weighted Spaces
Theorem
Boundedness

Citation

Ho, K.-P. (2016). Singular integral operators, john–nirenberg inequalities and triebel–lizorkin type spaces on weighted lebesgue spaces with variable exponents. Revista de la Unión Matemática Argentina, 57(1), 85-101.

Keywords

  • Singular integral
  • John–Nirenberg inequality
  • Triebel–Lizorkin spaces
  • Weight, variable exponent
  • Extrapolation