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- W2889035900 abstract "This paper will be devoted to study a class of bilinear square-function Fourier multiplier operator associated with a symbol $m$ defined by $$begin{eqnarray}displaystyle & & displaystyle mathfrak{T}_{unicode[STIX]{x1D706},m}(f_{1},f_{2})(x)nonumber displaystyle & & displaystyle quad =Big(iint _{mathbb{R}_{+}^{n+1}}Big(frac{t}{|x-z|+t}Big)^{nunicode[STIX]{x1D706}}nonumber displaystyle & & displaystyle qquad times ,bigg|int _{(mathbb{R}^{n})^{2}}e^{2unicode[STIX]{x1D70B}ixcdot (unicode[STIX]{x1D709}_{1}+unicode[STIX]{x1D709}_{2})}m(tunicode[STIX]{x1D709}_{1},tunicode[STIX]{x1D709}_{2})hat{f}_{1}(unicode[STIX]{x1D709}_{1})hat{f}_{2}(unicode[STIX]{x1D709}_{2}),dunicode[STIX]{x1D709}_{1},dunicode[STIX]{x1D709}_{2}bigg|^{2}frac{dz,dt}{t^{n+1}}Big)^{1/2}.nonumberend{eqnarray}$$ A basic fact about $mathfrak{T}_{unicode[STIX]{x1D706},m}$ is that it is closely associated with the multilinear Littlewood–Paley $g_{unicode[STIX]{x1D706}}^{ast }$ function. In this paper we first investigate the boundedness of $mathfrak{T}_{unicode[STIX]{x1D706},m}$ on products of weighted Lebesgue spaces. Then, the weighted endpoint $Llog L$ type estimate and strong estimate for the commutators of $mathfrak{T}_{unicode[STIX]{x1D706},m}$ will be demonstrated." @default.
- W2889035900 created "2018-09-07" @default.
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- W2889035900 date "2018-08-28" @default.
- W2889035900 modified "2023-10-18" @default.
- W2889035900 title "ON THE BILINEAR SQUARE FOURIER MULTIPLIER OPERATORS ASSOCIATED WITH FUNCTION" @default.
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- W2889035900 doi "https://doi.org/10.1017/nmj.2018.30" @default.
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