scholarly journals Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

2000 ◽  
Vol 143 (2) ◽  
pp. 121-144 ◽  
Author(s):  
A. Böttcher ◽  
M. Seybold
Keyword(s):  
Muckenhoupt Weight

scholarly journals Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yue Hu ◽  
Yueshan Wang
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Muckenhoupt Weight ◽  
Marcinkiewicz Integral ◽  
Smoothness Condition ◽  
Weight Class ◽  
Marcinkiewicz Integrals ◽  
Weak Hardy Space ◽  
Weak Lebesgue Space

We prove that, under the conditionΩ∈Lipα, Marcinkiewicz integralμΩis bounded from weighted weak Hardy spaceWHwpRnto weighted weak Lebesgue spaceWLwpRnformaxn/n+1/2,n/n+α<p≤1, wherewbelongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness ofμΩfromWHw1ℝntoWLw1Rn.

Embedding properties of weighted Besov-type spaces

2015 ◽  
Vol 13 (05) ◽  
pp. 507-553 ◽  
Author(s):  
Wen Yuan ◽  
Dorothee D. Haroske ◽  
Leszek Skrzypczak ◽  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Necessary Conditions ◽  
Muckenhoupt Weight ◽  
Exponential Weights ◽  
Special Cases ◽  
Type Spaces ◽  
Sufficient And Necessary Conditions ◽  
Weighted Besov Spaces ◽  
Dyadic Cubes ◽  
Besov Type Spaces

In this paper, we consider the embeddings of weighted Besov spaces [Formula: see text] into Besov-type spaces [Formula: see text] with w being a (local) Muckenhoupt weight, and give sufficient and necessary conditions on the continuity and the compactness of these embeddings. As special cases, we characterize the continuity and the compactness of embeddings in case of some polynomial or exponential weights. The proofs of these conclusions strongly depend on the geometric properties of dyadic cubes.

Lp Neumann problem for some Schrödinger equations in (semi-)convex domains

2019 ◽  
Vol 22 (02) ◽  
pp. 1950007
Author(s):  
Sibei Yang ◽  
Dachun Yang
Keyword(s):  
Neumann Problem ◽  
Convex Domain ◽  
Boundary Data ◽  
Muckenhoupt Weight ◽  
Weight Class ◽  
Convex Domains ◽  
Reverse Hölder Class ◽  
Special Cases ◽  
The Neumann Problem ◽  
Reverse Hölder

Let [Formula: see text], [Formula: see text] be a bounded (semi-)convex domain in [Formula: see text] and the non-negative potential [Formula: see text] belong to the reverse Hölder class [Formula: see text]. Assume that [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the Muckenhoupt weight class on [Formula: see text], the boundary of [Formula: see text]. In this paper, the authors show that, for any [Formula: see text], the Neumann problem for the Schrödinger equation [Formula: see text] in [Formula: see text] with boundary data in (weighted) [Formula: see text] is uniquely solvable. The obtained results in this paper essentially improve the known results which are special cases of the results obtained by Shen [Indiana Univ. Math. J. 43 (1994) 143–176] and Tao and Wang [Canad. J. Math. 56 (2004) 655–672], via extending the range [Formula: see text] of [Formula: see text] into [Formula: see text].

Toeplitz operators with semi-almost periodic symbols on spaces with Muckenhoupt weight

1994 ◽  
Vol 18 (3) ◽  
pp. 261-276 ◽  
Author(s):  
A. B�ttcher ◽  
Yu. I. Karlovich ◽  
I. M. Spitkovsky
Keyword(s):  
Toeplitz Operators ◽  
Muckenhoupt Weight ◽  
Almost Periodic

Fourier operators on weighted Hardy spaces

1987 ◽  
Vol 101 (1) ◽  
pp. 113-121
Author(s):  
Hans P. Heinig
Keyword(s):  
Fourier Transform ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Muckenhoupt Weight ◽  
Hardy’S Inequality ◽  
Weighted Hardy Spaces ◽  
Hardy's Inequality ◽  
The Fourier Transform

AbstractIn this note we utilize the atomic decomposition of weighted Hardy spaces to prove weighted versions of Hardy's inequality for the Fourier transform with Muckenhoupt weight. The result extends to certain integral operators with homogeneous kernels of degree −1.

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