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1
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Two-weight norm inequalities for potential type integral operators in the case p > q > 0 and p > 1

100%
Tanaka H.
Studia Mathematica
|
2013
|
tom 216
|
nr 1
1-15
EN
Sufficient conditions for a two-weight norm inequality for potential type integral operators to hold are given in the case p > q > 0 and p > 1 in terms of the Hedberg-Wolff potential.
2
Content available remote

The trilinear embedding theorem

100%
Tanaka H.
Studia Mathematica
|
2015
|
tom 227
|
nr 3
239-248
EN
Let $σ_{i}$, i = 1,2,3, denote positive Borel measures on ℝⁿ, let 𝓓 denote the usual collection of dyadic cubes in ℝⁿ and let K: 𝓓 → [0,∞) be a map. We give a characterization of a trilinear embedding theorem, that is, of the inequality $∑_{Q∈𝓓} K(Q)∏_{i=1}^{3} |∫_{Q} f_{i}dσ_{i}| ≤ C∏_{i=1}^{3} ||f_{i}||_{L^{p_{i}}(dσ_{i})}$ in terms of a discrete Wolff potential and Sawyer's checking condition, when 1 < p₁,p₂,p₃ < ∞ and 1/p₁ + 1/p₂ + 1/p₃ ≥ 1.
3
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The John-Nirenberg type inequality for non-doubling measures

63%
Sawano Y., Tanaka H.
Studia Mathematica
|
2007
|
tom 181
|
nr 2
153-170
EN
X. Tolsa defined a space of BMO type for positive Radon measures satisfying some growth condition on $ℝ^{d}$. This new BMO space is very suitable for the Calderón-Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces.
4
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Weighted norm inequalities for multilinear fractional operators on Morrey spaces

51%
Iida T., Sato E., Sawano Y., Tanaka H.
Studia Mathematica
|
2011
|
tom 205
|
nr 2
139-170
EN
A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
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