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One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2014)

Banach Center Publications

We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.

Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues

Jean-Pierre Roth (1976)

Annales de l'institut Fourier

Soit X un espace localement compact. Tout opérateur dissipatif de domaine dense dans C 0 ( ( X ) est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où X est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur C 0 ( X ) se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur C 0 ( X ) .À tout opérateur A vérifiant le principe du maximum positif sur C 0 ( X , R ) et de domaine assez riche, on associe un opérateur bilinéaire B , appelé...

Operators determining the complete norm topology of C(K)

A. Villena (1997)

Studia Mathematica

For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and x 0 A , we show that every complete norm on A which makes continuous the multiplication by x 0 is equivalent to · provided that x 0 - 1 ( λ ) has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).

Operators on Lorentz sequence spaces

Subhash Chander Arora, Gopal Datt, Satish Verma (2009)

Mathematica Bohemica

Description of multiplication operators generated by a sequence and composition operators induced by a partition on Lorentz sequence spaces l ( p , q ) , 1 < p , 1 q is presented.

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