Did both Jonathan Franzen and Vladimir Nabokov earn recognition for writing in their native language?
no
Vladimir Nabokov
Vladimir Vladimirovich Nabokov ( ; Russian: Влади́мир Влади́мирович Набо́ков , ] , also known by the pen name Vladimir Sirin; (April 22nd, 1899 — July 2nd, 1977) was a Russian-American novelist and entomologist.
 His first nine novels were in Russian, but he achieved international prominence after he began writing English prose.
Jonathan Franzen
Jonathan Earl Franzen (born August 17, 1959) is an American novelist and essayist.
 His 2001 novel "The Corrections", a sprawling, satirical family drama, drew widespread critical acclaim, earned Franzen a National Book Award, was a Pulitzer Prize for Fiction finalist, earned a James Tait Black Memorial Prize and was shortlisted for the International IMPAC Dublin Literary Award.
 His novel "Freedom" (2010) garnered similar praise and led to an appearance on the cover of "Time" magazine alongside the headline "Great American Novelist".
Why Bother? (essay)
"Why Bother?"
, originally published as "Perchance to Dream: In the Age of Images, a Reason to Write Novels", is a literary essay by American novelist Jonathan Franzen.
 It is often referred to as "The Harper's Essay".
 First published in the April 1996 issue of "Harper's" magazine, the essay concerns the persistence of reading within the context of technological growth and distraction.
 Franzen recounts his meditations on the state and possibility of the novel form, often against the backdrop of his personal experience, eventually concluding that the novel still has potential cultural agency in the United States, and often gains it by paradoxical drives of both culture and author. Nabokov's Congeries
Nabokov's Congeries was a collection of work by Vladimir Nabokov published in 1968 and reprinted in 1971 as "The Portable Nabokov".
 Because Nabokov supervised its production less than a decade before he died, it is useful in attempting to identify which works Nabokov considered to be his best, especially among his short stories. The Stories of Vladimir Nabokov
The Stories of Vladimir Nabokov (in some British editions, The Collected Stories) is a posthumous collection of every known short story that Vladimir Nabokov ever wrote, with the exception of "The Enchanter".
 The thirteen stories not previously published in English are translated by the author's son, Dmitri Nabokov.
 The collection was first published in America by Alfred A. Knopf in 1995. The Vane Sisters
"The Vane Sisters" is a short story by Vladimir Nabokov, written in March 1951.
 It is famous for providing one of the most extreme examples of an unreliable narrator.
 It was first published in the Winter 1958 issue of "The Hudson Review" and then reprinted in "Encounter" during 1959.
 The story was included in "Nabokov's Quartet" (1966), "Nabokov's Congeries" (1968; reprinted as "The Portable Nabokov", 1971), "Tyrants Destroyed and Other Stories" (1975), and "The Stories of Vladimir Nabokov" (1995). The Waltz Invention
The Waltz Invention is a tragicomedy in three acts written by Vladimir Nabokov in Russian as "Izobretenie Val'sa" in 1938.
 It was first published in "Russkie Zapiski" in Paris in the same year.
 Nabokov translated it at that time into English for the first time.
 The second English translation was made by Dmitri Nabokov in 1964 with the help of his father who also made some alterations; it was published in 1966.
 The play takes place in an unnamed country in about 1935.
 Nabokov makes the point in the 1965 written foreword that while the work sounds a "prophetic forenote" - the invention is a weapon of mass destruction -, he has no political message and does not support the peaceniks of his time. Rozhdestveno Memorial Estate
The Rozhdestveno Memorial Estate is a writer's house museum and park near Siverskaya, Gatchinsky District, Leningrad Oblast, that commemorates the most famous owner of the estate, Vladimir Nabokov; the Batovo and Vyra estates, also immortalized by Nabokov, are nearby.
 As Nabokov spent part of his youth at Vyra, he visited his grandmother at Batovo and his uncle at Rozhdestveno.
 The Batovo mansion burned down in 1925, Vyra was destroyed in 1944, leaving Rozhdestveno as the sole survivor of the triad of estates owned by the Nabokov family. Bachmann (short story)
"Bachmann" is a short story written in Russian by Vladimir Nabokov under his nom-de-plume V. Sirin in Berlin in 1924.
 It was first published in Rul, a Russian émigré paper founded by his father, Vladimir Dmitrievich Nabokov, and later included in a number of short story collections: "Vozvrashchenie Chorba", "Tyrants Destroyed and Other Stories" (1975), and "The Stories of Vladimir Nabokov" (1995).
 He and his son, Dmitri Nabokov, provided the English translation. PEN/Nabokov Award
The PEN/Nabokov Award for Achievement in International Literature is awarded biannually by the PEN American Center to writers, principally novelists, "whose works evoke to some measure Nabokov's brilliant versatility and commitment to literature as a search for the deepest truth and the highest pleasure— what Nabokov called the 'indescribable tingle of the spine'."
 The winner is awarded $50,000 as of 2016.
 The award is financed by the Vladimir Nabokov Foundation, founded by Dmitri Nabokov.
 It has been called one of the most prestigious PEN prizes.