Displaying similar documents to “Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in R²”

Endpoint multiplier theorems of Marcinkiewicz type.

Terence Tao, James Wright (2001)

Revista Matemática Iberoamericana

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We establish sharp (H,L) and local (L logL,L) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H to L and L logL to L, and that these estimates are sharp.

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Ferenc Weisz (1996)

Studia Mathematica

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The martingale Hardy space H p ( [ 0 , 1 ) 2 ) and the classical Hardy space H p ( 2 ) are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from H p to L p (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified...