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Entropy bump conditions for fractional maximal and integral operators

100%

Rahm R., Spencer S.

Concrete Operators

2016

tom 3

nr 1

112-121

We investigate weighted inequalities for fractional maximal operators and fractional integral operators.We work within the innovative framework of “entropy bounds” introduced by Treil–Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.

Commutators with fractional integral operators

81%

Holmes I., Rahm R., Spencer S.

Studia Mathematica

2016

tom 233

nr 3

279-291

We investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $μ,λ ∈ A_{p,q}$ and α/n + 1/q = 1/p, the norm $||[b,I_{α}]: L^{p}(μ^{p}) → L^{q}(λ^{q})||$ is equivalent to the norm of b in the weighted BMO space BMO(ν), where $ν = μλ^{-1}$. This work extends some of the results on this topic existing in the literature, and continues a line of investigation which was initiated by Bloom in 1985 and was recently developed further by the first author, Lacey, and Wick.

Ograniczanie wyników

1 Concrete Operators

1 Studia Mathematica

2 Rahm R.

2 Spencer S.

1 Holmes I.

2 2016

Wyniki wyszukiwania

Entropy bump conditions for fractional maximal and integral operators

Commutators with fractional integral operators