Displaying similar documents to “An estimate of the conjugate functions”

On the L 1 norm of exponential sums

S. K. Pichorides (1980)

Annales de l'institut Fourier

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The L 1 norm of a trigonometric polynomial with N non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of C ( log N ) / ( log log N ) 2 .

On weak type inequalities for rare maximal functions

K. Hare, A. Stokolos (2000)

Colloquium Mathematicae

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The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.

Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds, Petr Gurka, Bohumír Opic (1995)

Studia Mathematica

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This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.