STRONGLY SINGULAR CONVOLUTION OPERATORS ON MODULATION SPACES

2011 ◽  
Vol 09 (05) ◽  
pp. 759-772 ◽  
Author(s):  
MEIFANG CHENG ◽  
ZHENQIU ZHANG
Keyword(s):  
Modulation Spaces ◽  
Convolution Operators ◽  
Lebesgue Spaces

The purpose of this paper is to investigate the mapping properties of the strongly singular convolution operators on general weighted modulation spaces [Formula: see text] for 0 < p ≤ ∞, 0 < q ≤ ∞ and s ∈ ℝ. Our results show that modulation spaces are good substitutions for Lebesgue spaces.

Singular convolution operators on Wiener amalgam spaces

2015 ◽  
Vol 13 (01) ◽  
pp. 1550003
Author(s):  
Meifang Cheng
Keyword(s):  
Modulation Spaces ◽  
Convolution Operators ◽  
Lebesgue Spaces ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

The purpose of this paper is to investigate some properties of the Wiener amalgam spaces. As applications, we study the boundedness properties of some singular convolution operators on such spaces. From our results, we will see that, besides modulation spaces, Wiener amalgam spaces are another good substitutions for Lebesgue spaces.

scholarly journals Two-weight inequalities for singular integral operators satisfying a variant of Hörmander's condition

2009 ◽  
Vol 7 (1) ◽  
pp. 43-59 ◽  
Author(s):  
Vagif S. Guliyev
Keyword(s):  
Singular Integral ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Convolution Operators ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Hörmander’S Condition

In this paper, we present some sufficient conditions for the boundedness of convolution operators that their kernel satisfies a certain version of Hörmander's condition, in the weighted Lebesgue spacesLp,ω(ℝn).

scholarly journals On Compactness of Embeddings of Fourier-Lebesgue Spaces into Modulation Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yevgeniy V. Galperin
Keyword(s):  
Modulation Spaces ◽  
Lebesgue Spaces

It is shown that, for a certain range of parameters, embeddings of Fourier-Lebesgue Lap∩ℱLbq spaces into modulation spaces Mα,βr, s are compact.

scholarly journals ON THE COMPLEXITY OF CLASSIFYING LEBESGUE SPACES

2020 ◽  
pp. 1-35
Author(s):  
TYLER A. BROWN ◽  
TIMOTHY H. MCNICHOLL ◽  
ALEXANDER G. MELNIKOV
Keyword(s):  
Lebesgue Spaces

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

Sign in / Sign up

Export Citation Format

Share Document