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Hankel multipliers and transplantation operators

Krzysztof Stempak, Walter Trebels (1997)

Studia Mathematica

Connections between Hankel transforms of different order for L p -functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

Péter Simon, Ferenc Weisz (1997)

Studia Mathematica

Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) ( k = 1 j = 1 | f ̂ ( k , j ) | p ( k j ) p - 2 ) 1 / p C p f H * * p (1/2 < p≤2) where f belongs to the Hardy space H * * p ( G m × G s ) defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.

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