127 research outputs found
Hausdorff operators on the Sobolev spaces
This paper is served as a first contribution regarding the boundedness of
Hausdorff operators on function spaces with smoothness. The sharp conditions
are established for boundedness of Hausdorff operators on Sobolev spaces
. As applications, some bounded and unbounded properties of Hardy
operator and adjoint Hardy operator on are deduced
On relatively compact sets in quasi-Banach function spaces
This paper is devoted to the study of the relatively compact sets in
Quasi-Banach function spaces, providing an important improvement of the known
results. As an application, we take the final step in establishing a relative
compactness criteria for function spaces with any weight without any
assumption.Comment: To appear in Proc. Amer. Math. So
Unimodular multipliers on -modulation spaces: A revisit with new method under weaker conditions
By a new method derived from Nicola--Primo--Tabacco[24], we study the
boundedness on -modulation spaces of unimodular multipliers with symbol
. Comparing with the previous results, the boundedness result is
established for a larger family of unimodular multipliers under weaker
assumptions
The unified theory for the necessity of bounded commutators and applications
The general methods which are powerful for the necessity of bounded
commutators are given. As applications, some necessary conditions for bounded
commutators are first obtained in certain endpoint cases, and several new
characterizations of space, Lipschitz spaces and their weighted versions
via boundedness of commutators in various function spaces are deduced.Comment: Some minor issue have been revise
Hausdorff operators on modulation and Wiener amalgam spaces
We give the sharp conditions for boundedness of Hausdorff operators on
certain modulation and Wiener amalgam spaces.Comment: To appear in "Annals of Functional Analysis
Characterization of Some Properties on Weighted Modulation Spaces
In this paper, some properties on weighted modulation and Wiener amalgam
spaces are characterized by the corresponding properties on weighted Lebesgue
spaces. As applications, sharp conditions for product inequalities, convolution
inequalities and embedding on weighted modulation and Wiener amalgam spaces are
obtained. These applications improve and extend many known results
Boundedness and compactness of commutators associated with Lipschitz functions
Let , and be a
singular or fractional integral operator with homogeneous kernel . In
this article, a CMO type space is introduced
and studied. In particular, the relationship between and the Lipchitz space is discussed. Moreover,
a necessary condition of restricted boundedness of the iterated commutator
on weighted Lebesgue spaces via functions in
, and an equivalent characterization of the
compactness for via functions in are obtained. Some results are new even in the
unweighted setting for the first order commutators.Comment: arXiv admin note: text overlap with arXiv:1712.0829
Full Characterization of embedding relations between alpha modulation spaces
In this paper, we consider the embedding relations between any two %
-modulation spaces. Based on an observation that the -modulation space
with smaller can be regarded as a corresponding % -modulation
space with larger , we give a complete characterization of the Fourier
multipliers between -modulation spaces with different . Then we
establish a full version of optimal embedding relations between
-modulation spaces. As an application, we determine that the bounded
operators commuting with translations between -modulation spaces are of
convolution type
On the compactness of oscillation and variation of commutators
In this paper, we first establish the weighted compactness result for
oscillation and variation associated with the truncated commutator of singular
integral operators. Moreover, we establish a new
characterization via the compactness of oscillation and variation of
commutators on weighted Lebesgue spaces
Limiting weak-type behaviors for factional maximal operators and fractional integrals with rough kernel
By a reduction method, the limiting weak-type behaviors of factional maximal
operators and fractional integrals are established without any smoothness
assumption on the kernel, which essentially improve and extend previous
results. As a byproduct, we characterize the boundedness of several operators
by the membership of their kernel in Lebesgue space on sphere.Comment: Some typos are correcte
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