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We develop a transference method to obtain theL    p-continuity of the Gaussian-Littlewood-Paley    g   -function and theL    p-continuity of the Laguerre-Littlewood-Paley    g   -function from theL    p-continuity of the Jacobi-Littlewood-Paley    g   -function, in dimension one, using the well-known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials.

journal of function spaces

A Transference Result of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>-Continuity of the Jacobi Littlewood-Paley <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-Function to the Gaussian and Laguerre Littlewood-Paley <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id…

A Transference Result of the Lp-Continuity of the Jacobi Littlewood-Paley g-Function to the Gaussian and Laguerre Littlewood-Paley