H¨ ormander-Mihlin-multiplierek
6. fejezet Jel¨ ol´ esek
An a 2−n hossz´us´ag´u diadikus intervallumok ´altal gener´alt σ-algebra BMO[0,1) a diadikus BMO t´er
BMO[0,1) a BMO t´er a [0, 1) intervallumon BMOR a BMO t´er a val´os sz´amok halmaz´an
BMO[0,∞) a Telyakovski˘ı-f´ele BMO t´er a nemnegat´ıv val´os sz´amok halmaz´an C a komplex sz´amok halmaza
DΦn aΦ ortonorm´alt rendszer n-edik Dirichlet-f´ele magf¨uggv´enye DΦn aΦ ortonorm´alt rendszer els˝o n elem´enek az ¨osszege
DeTn az n-edik konjug´alt trigonometrikus Dirichlet-magf¨uggv´eny
∆a az a sorozat differencia sorozata
ek az ek(t) =eikt (k∈Z, t∈R) komplex trigonometrikus f¨uggv´eny EΦn a Φ rendszer szerinti legjobb k¨ozel´ıt´es oper´atora
En a felt´eteles v´arhat´o ´ert´ek oper´ator
f˜ az f f¨uggv´eny trigonometrikus konjug´alt f¨ugg´enye fcΦ aΦ ortonorm´alt rendszer szerinti Fourier-transzform´alt Hp[0,1) a diadikus Hardy-terek a [0, 1)intervallumon
Hp[0,1)2 a k´etdimenzi´os diadikus Hardy-terek a [0, 1)2 egys´egn´egyzeten H][0,1)2 a k´etdimenzi´os hibrid diadikus Hardy-t´er a [0, 1)2 egys´egn´egyzeten Hp,r[0,1)2 a diadikus Hardy-Lorentz-terek az egys´egn´egyzeten
Hp[0,∞) a diadikus Hardy-terek a nemnegat´ıv val´os sz´amok halmaz´an
Hs[0,∞) a meg´all´ıtott diadikus Hardy-t´er a nemnegat´ıv val´os sz´amok halmaz´an H2π a val´os, 2π szerint periodikus Hardy-t´er
H[0,1) a val´os nemperiodikus Hardy-t´er a [0, 1) intervallumon H?[0,1) az ´atrendez´esre invari´ans Hardy-t´er
HR a klasszikus val´os Hardy-t´er a val´os sz´amok halmaz´an
H[0,∞) a Telyakovski˘ı-f´ele Hardy-t´er a nemnegat´ıv val´os sz´amok halmaz´an
148 Jel¨ol´esek
Hf az f f¨uggv´eny Hilbert-transzform´altja χA az A halmaz karakterisztikus f¨uggv´enye L(An) az An-m´erhet˝o f¨uggv´enyek halmaza
LpA az A⊂R halmazon ´ertelmezett Lebesgue-t´er Lp,r[0,1)2 a Lebesgue-Lorentz-terek az egys´egn´egyzeten
Lp,loc[0,∞) azon f¨uggv´enyek halmaza, amelyek minden v´eges m´ert´ek˝uA⊂[0,∞) eset´enLpA-ban vannak
LM az M Young-f¨uggv´eny ´altal gener´alt Orlicz-t´er N a term´eszetes sz´amok halmaza
P a pozit´ıv term´eszetes sz´amok halmaza PnΦ a legfeljebb n-edfok´u Φ-polinomok halmaza Qf az f marting´al, f¨uggv´eny kvadratikus vari´aci´oja R a val´os sz´amok halmaza
SΦn a Φ ortonorm´alt rendszer szerinti n-edik Fourier-r´eszlet¨osszeg
σΦnf az ff¨uggv´eny Φ-rendszer szerinti Fourier-sor´anak az n-edik Fej´er-k¨ozepe Tϕ a ϕ ´altal gener´alt multiplier oper´ator
TN a Telyakovski˘ı-transzform´aci´o sorozatokon TR a Telyakovski˘ı-transzform´aci´o a sz´amegyenesen V(n) az n bin´aris jegyeinek a vari´aci´oja
Vr,nΦ f az f f¨uggv´eny Φ rendszer szerinti ´altal´anos´ıtott de la Vall´ee Poussin-k¨ozepe [x] az x val´os sz´am eg´esz r´esze
Z az eg´esz sz´amok halmaza
u diadikus ¨osszead´as a [0, 1) intervallumon
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