Characterization of $$H^1$$H1 Sobolev Spaces by Square Functions of Marcinkiewicz Type
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DOI: 10.1007/s00041-018-9618-2
Abstract: We establish characterization of $$H^1$$H1 Sobolev spaces by certain square functions of Marcinkiewicz type. The square functions are related to the Lusin area integrals. Also, in the one dimensional case, the non-periodic version of the… read more here.
Keywords: marcinkiewicz type; characterization sobolev; sobolev spaces; square functions ... See more keywords
Twisted symmetric square L-functions for $$\mathrm {GL}_n$$GLn and invariant trilinear forms
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DOI: 10.1007/s00209-016-1726-6
Abstract: Following the works of Bump and Ginzburg and of Takeda, we develop a theory of twisted symmetric square L-functions for $$\mathrm {GL}_n$$GLn. We characterize their pole in terms of certain trilinear period integrals, determine all… read more here.
Keywords: symmetric square; invariant trilinear; square functions; twisted symmetric ... See more keywords
Subdyadic square functions and applications to weighted harmonic analysis
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DOI: 10.1016/j.aim.2016.11.018
Abstract: Abstract Through the study of novel variants of the classical Littlewood–Paley–Stein g -functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on R d satisfying regularity hypotheses adapted to fine (subdyadic) scales.… read more here.
Keywords: subdyadic square; harmonic analysis; functions applications; weighted harmonic ... See more keywords
Compactness of the commutators of intrinsic square functions on weighted Lebesgue spaces
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DOI: 10.3906/mat-1702-10
Abstract: where Γβ(x) = {(y, t) ∈ R + : |x− y| < βt}. Denote Gα,1(f) = Gα(f) . The intrinsic square functions were first introduced by Wilson in order to answer a conjecture proposed by… read more here.
Keywords: square functions; weighted lebesgue; intrinsic square; compactness commutators ... See more keywords