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In this paper, the authors prove the boundedness of commutators generated by the weighted Hardy operator on weighted $lambda$-central Morrey space with the weight $omega$ satisfying the doubling condition. Moreover, the authors give the characterization for the weighted $lambda$-central Campanato space by introducing a new kind of operator which is related to the commutator of weighted Hardy operator.
We revisit weighted Hardy-type inequalities employing an elementary ad hoc approach that yields explicit constants. We also discuss the infinite sequence of power weighted Birman-Hardy-Rellich-type inequalities and derive an operator-valued version thereof.
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
We study the two-weighted estimate [ bigg|sum_{k=0}^na_k(x)int_0^xt^kf(t)dt|L_{q,v}(0,infty)bigg|leq c|f|L_{p,u}(0,infty)|,tag{$*$} ] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<pleq qleqinfty$, prov
This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-H{o}rmander conditions. As applications, we obtain the strong type quantitative weighted bounds for such
The principal aim of this paper is to extend Birmans sequence of integral inequalities originally obtained in 1961, and containing Hardys and Rellichs inequality as special cases, to a sequence of inequalities that incorporates power weights on eithe