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We introduce new classes of weights and   B  M  O   functions associated with a nondecreasing function    ϕ    of upper type    β    with   β  &gt;  0   and obtain the weighted norm inequalities for Calderón-Zygmund operators of    ϕ   -type and their commutators.

journal of function spaces

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> Weights, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>B</mml:mi><mml:mi>M</mml:mi><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, and …

Ap(ϕ) Weights, BMO(ϕ), and …