All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 26 Next

Displaying 501 – 520 of 561

Showing per page

Ondelettes et poids de Muckenhoupt

Pierre Lemarié-Rieusset (1994)

Studia Mathematica

We study, for a basis of Hölderian compactly supported wavelets, the boundedness and convergence of the associated projectors P j on the space L p ( d μ ) for some p in ]1,∞[ and some nonnegative Borel measure μ on ℝ. We show that the convergence properties are related to the A p criterion of Muckenhoupt.

Ondelettes generalisées et fonctions d'échelle à support compact.

Pierre-Gilles Lemarié-Rieusset (1993)

Revista Matemática Iberoamericana

We show that to any multi-resolution analysis of L2(R) with multiplicity d, dilation factor A (where A is an integer ≥ 2) and with compactly supported scaling functions we may associate compactly supported wavelets. Conversely, if (Ψε,j,k = Aj/2 Ψε (Ajx - k)), 1 ≤ ε ≤ E and j, k ∈ Z, is a Hilbertian basis of L2(R) with continuous compactly supported mother functions Ψε, then it is provided by a multi-resolution analysis with dilation factor A, multiplicity d = E / (A - 1) and with compactly supported...

One-sided discrete square function

A. de la Torre, J. L. Torrea (2003)

Studia Mathematica

Let f be a measurable function defined on ℝ. For each n ∈ ℤ we consider the average A ₙ f ( x ) = 2 - n ∫ x x + 2 ⁿ f . The square function is defined as S f ( x ) = ( ∑ n = - ∞ ∞ | A ₙ f ( x ) - A n - 1 f ( x ) | ² ) 1 / 2 . The local version of this operator, namely the operator S ₁ f ( x ) = ( ∑ n = - ∞ 0 | A ₙ f ( x ) - A n - 1 f ( x ) | ² ) 1 / 2 , is of interest in ergodic theory and it has been extensively studied. In particular it has been proved [3] that it is of weak type (1,1), maps L p into itself (p > 1) and L ∞ into BMO. We prove that the operator S not only maps L ∞ into BMO but it also maps BMO into BMO. We also prove that the L p boundedness still holds...

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.

Open problems in constructive function theory.

Baratchart, L., Martínez-Finkelshtein, A., Jimenez, D., Lubinsky, D.S., Mhaskar, H.N., Pritsker, I., Putinar, M., Stylianopoulos, N., Totik, V., Varju, P., Xu, Y. (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Currently displaying 501 – 520 of 561